The generator matrix

 1  1  1  1  1  1  1  1  X  1  0  1  1  1  1 X^3  1  X  X  1  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^3+X^2+X X^3  X X^3+X X^3+X^2 X^2+X  0  X X^3 X^2+X  X X^3+X  X  0
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3 X^2 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 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+40x^18+92x^19+233x^20+424x^21+499x^22+418x^23+205x^24+88x^25+31x^26+7x^28+5x^30+2x^31+2x^32+1x^34

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.