The generator matrix
1 0 0 1 1 1 X^2+2 X^2+2 X^2 X 1
0 1 0 1 X X^2+X+1 0 1 X^2 1 2
0 0 1 1 1 0 1 1 X X^2+X+2 0
0 0 0 X 2 X+2 X^2+X X^2 X^2+X X+2 X^2
generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 7.
Homogenous weight enumerator: w(x)=1x^0+98x^7+591x^8+2576x^9+7285x^10+11588x^11+7466x^12+2496x^13+522x^14+138x^15+6x^16+1x^18
The gray image is a code over GF(2) with n=88, k=15 and d=28.
This code was found by Heurico 1.16 in 0.797 seconds.