The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+7x^6+24x^7+90x^8+60x^9+547x^10+600x^11+536x^12+64x^13+85x^14+16x^15+13x^16+4x^17+1x^18

The gray image is a linear code over GF(2) with n=88, k=11 and d=24.
This code was found by Heurico 1.16 in 0.015 seconds.