The generator matrix

 1  0  0  0  1  1  1  1  1  0  1
 0  1  0  0 X+1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1 X^3+X+1  1  0
 0  0  1  0  1  0 X^2  X  1 X^2+X  0
 0  0  0  1  1 X+1 X^2+X  1 X^2+1  1  0
 0  0  0  0 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^2 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+89x^6+920x^7+4160x^8+17412x^9+56159x^10+104592x^11+56204x^12+17544x^13+4103x^14+824x^15+115x^16+20x^17+1x^18

The gray image is a linear code over GF(2) with n=88, k=18 and d=24.
This code was found by Heurico 1.16 in 31 seconds.