The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  X  1  1  0  X X^2
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^2+X  X  0 X^3+X^2 X^3 X^3+X X^2+X X^2+X X^3+X  0 X^3+X  X X^2 X^3
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  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+99x^18+32x^19+251x^20+352x^21+594x^22+352x^23+246x^24+32x^25+68x^26+12x^28+6x^30+1x^32+1x^34+1x^36

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 6.98 seconds.