The generator matrix

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

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+23x^18+44x^19+32x^20+288x^21+278x^22+256x^23+25x^24+48x^25+18x^26+4x^27+6x^28+1x^42

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.