The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 X^2  1  1  1  1 X^2  1
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3  0  0 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3  0 X^2 X^2  0 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 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+24x^18+44x^19+112x^20+152x^21+379x^22+160x^23+98x^24+8x^25+12x^26+20x^27+12x^28+1x^32+1x^38

The gray image is a linear code over GF(2) with n=176, k=10 and d=72.
This code was found by Heurico 1.16 in 0.016 seconds.