The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 X^2+2 1
0 X 0 X 2 0 X^2+X X^2+X X^2 X^2+2 X^2+X X^2+X+2 X+2 X^2+X X^2+2 X^2+2 X+2 X^2+X X^2+2 X 0
0 0 X X X^2 X^2+X X^2+X 0 X^2+2 0 2 X^2 X+2 X^2+X+2 X^2+X+2 X+2 X^2 X+2 X^2+2 X^2+X X^2+X
0 0 0 2 2 2 0 2 0 2 0 0 0 2 2 0 0 0 2 2 0
generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+163x^18+140x^19+354x^20+764x^21+357x^22+100x^23+125x^24+20x^25+23x^26+1x^38
The gray image is a code over GF(2) with n=168, k=11 and d=72.
This code was found by Heurico 1.16 in 0.25 seconds.