The generator matrix
1 1 1 1 1 1 X^3 X X X 1
0 X 0 X X^3 0 X^2 X X^3+X X^3+X^2 X^3+X
0 0 X X X^2 X^2+X X X 0 X^3+X X
0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0
generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+37x^8+260x^9+376x^10+718x^11+378x^12+218x^13+40x^14+18x^15+2x^17
The gray image is a linear code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.