The generator matrix

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

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+112x^18+40x^19+285x^20+344x^21+528x^22+344x^23+233x^24+40x^25+88x^26+23x^28+8x^30+2x^32

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 0.047 seconds.