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.