The generator matrix

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

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+98x^7+591x^8+2576x^9+7285x^10+11588x^11+7466x^12+2496x^13+522x^14+138x^15+6x^16+1x^18

The gray image is a linear code over GF(2) with n=88, k=15 and d=28.
This code was found by Heurico 1.16 in 1.02 seconds.