The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X^2+X  1  1  1 X^3+X  1  1 X^3  1  1  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^2+X+1 X^3  1 X^2+1  1 X^3+X X^3+X^2  1  1 X^3+X^2+X X+1  1 X^3 X^3+X^2+X X^2  0
 0  0 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3 X^2 X^3  0 X^2  0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^2  0
 0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  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+31x^18+204x^19+385x^20+1100x^21+707x^22+1064x^23+377x^24+168x^25+29x^26+12x^27+3x^28+12x^29+1x^30+2x^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 0.062 seconds.