The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+32x^7+95x^8+288x^9+928x^10+1408x^11+935x^12+288x^13+80x^14+32x^15+8x^16+1x^20

The gray image is a linear code over GF(2) with n=88, k=12 and d=28.
This code was found by Heurico 1.16 in 0.031 seconds.