The generator matrix

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

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+132x^18+176x^19+506x^20+732x^21+1060x^22+712x^23+462x^24+160x^25+116x^26+8x^27+22x^28+4x^29+4x^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 0.079 seconds.