The generator matrix

 1  1  1  1  1  1  1  1  1  1  X X^3  1  1  1  0  X  1  0  X  1  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^3+X^2+X  X X^2 X^2 X^2+X  X X^3 X^3+X^2+X  X X^3+X^2 X^3+X^2  0
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2  0 X^3+X^2
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^2  0 X^3  0 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 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+180x^18+92x^19+498x^20+672x^21+1248x^22+696x^23+454x^24+64x^25+132x^26+12x^27+38x^28+8x^30+1x^32

The gray image is a linear code over GF(2) with n=176, k=12 and d=72.
This code was found by Heurico 1.16 in 8.25 seconds.