The generator matrix
1 0 0 1 1 1 X+2 2 1 1
0 1 0 X X^2+1 X^2+X+1 1 1 X^2+X+2 X^2+2
0 0 1 1 X+1 X X^2+1 X X^2+X+1 0
0 0 0 2 2 0 0 2 0 2
generates a code of length 10 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 7.
Homogenous weight enumerator: w(x)=1x^0+98x^7+641x^8+1538x^9+3652x^10+1530x^11+622x^12+94x^13+12x^14+4x^15
The gray image is a code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.063 seconds.