The generator matrix

 1  1  1  1  1  1  X  X  X  1  1
 0  X  0  X X^3  0  X X^2+X X^2 X^3 X^2
 0  0  X  X X^2 X^2+X  X X^2  X X^2+X  0
 0  0  0 X^2  0 X^3  0 X^2 X^3 X^2 X^2

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+178x^8+216x^9+968x^10+1368x^11+992x^12+200x^13+152x^14+8x^15+13x^16

The gray image is a linear code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.75 seconds.