The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X 2X X X X 0 X X X 2X 0 0 2X X X 2X 0 2X 0 X X X 2X 0 0 0 2X X 0 2X X 0 0 0 X X 2X X 0 X 0 2X 0 2X 2X X 0 X X X X 2X X 2X 0 X 0 0 X X 2X 2X X 2X X
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 X X 2X 2X 2X 2X 2X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 0 X X 0 0 X X 2X 0 0 X 2X X X 0 0 0 2X 0 0 X 2X 2X 2X 2X 2X 2X 0 X X X X 2X 2X 0 X X X 2X X X 2X 2X
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X X 2X 2X 2X 0 X 0 0 2X 2X 0 2X X X 0 0 X X 2X 2X 0 0 X 0 0 X X 2X 2X X 2X 2X 0 X 2X 0 X X 0 X 2X 0 0 X X 0 0 X X 0 X 2X 0 X
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X X 0 0 0 X 0 0 2X X X X 0 0 2X 0 2X 2X 2X 0 2X X X 2X 0 X X 2X X 0 2X 2X X X X 0 2X 0 0 0 0 2X 2X 0 X 0 0 2X X 2X 0 2X 2X 0 0 X 2X X 2X 0 X 0 X X 2X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 2X X X 2X 2X X 0 0 2X 2X 2X 2X 0 0 2X X 0 2X 0 2X X 2X 0 X X 2X X 0 0 2X 2X 0 X X X 0 X X 0 X 2X 0 0 0 0 X X 0 0 0 2X X X 2X 0 X 2X 0 X 0 2X 2X X 0
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X X X X X 2X 0 0 X 2X 0 X 2X 2X X X 2X 2X 0 X 2X X 0 X 0 0 X 2X X X X X 0 X X 0 2X 2X 0 2X 2X 0 0 0 2X 0 2X X 0 0 0 0 X 2X 2X 2X X 2X 0 0 2X 0 2X X X
generates a code of length 87 over Z3[X]/(X^2) who´s minimum homogenous weight is 156.
Homogenous weight enumerator: w(x)=1x^0+120x^156+154x^159+254x^162+300x^165+564x^168+1142x^171+1610x^174+1306x^177+526x^180+108x^183+98x^186+92x^189+90x^192+72x^195+50x^198+40x^201+16x^204+12x^207+2x^213+2x^222+2x^243
The gray image is a linear code over GF(3) with n=261, k=8 and d=156.
This code was found by Heurico 1.16 in 1.88 seconds.