The generator matrix

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

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+26x^7+60x^8+90x^9+202x^10+1300x^11+188x^12+100x^13+52x^14+18x^15+7x^16+2x^17+2x^18

The gray image is a linear code over GF(2) with n=88, k=11 and d=28.
This code was found by Heurico 1.16 in 0.015 seconds.