The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+34x^18+110x^19+166x^20+404x^21+646x^22+408x^23+129x^24+92x^25+36x^26+10x^27+8x^28+3x^30+1x^38

The gray image is a linear code over GF(2) with n=176, k=11 and d=72.
This code was found by Heurico 1.16 in 0.031 seconds.