The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1 X^2  1 X^2  X  1 X^2
 0 X^3+X^2  0  0  0 X^3+X^2 X^2 X^2 X^3 X^2  0 X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^3  0 X^2 X^3+X^2 X^2
 0  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2 X^3  0 X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2
 0  0  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 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+117x^18+64x^19+266x^20+192x^21+800x^22+192x^23+230x^24+64x^25+98x^26+14x^28+8x^30+1x^32+1x^34

The gray image is a linear code over GF(2) with n=176, k=11 and d=72.
This code was found by Heurico 1.16 in 21.9 seconds.