The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  X X^2  X  X
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^2 X^3  0 X^3+X^2 X^3  0 X^2 X^3+X^2  0 X^3 X^2 X^2 X^3
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0 X^3 X^3  0 X^3+X^2 X^2 X^2 X^2  0
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2 X^3 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3  0  0 X^3 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+32x^18+48x^19+59x^20+216x^21+333x^22+210x^23+56x^24+24x^25+18x^26+12x^27+11x^28+1x^30+2x^31+1x^32

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 0.015 seconds.