The generator matrix

 1  1  1  1  1  X  X  X  X  X  X
 0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0
 0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+6x^9+6x^10+104x^11+6x^12+2x^14+1x^16+2x^17

The gray image is a linear code over GF(2) with n=88, k=7 and d=36.
This code was found by Heurico 1.16 in -6.48e-008 seconds.