The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  0  1  1 X^2+X  1  1  1  1 X^3  1  X  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X+1  0  1 X^3+1 X^3+X^2+X  1 X^2+X X^2 X^3+X^2+1 X^3+X^2+X  1 X+1  1  X X^2+X+1 X^3
 0  0 X^2  0  0 X^3  0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0 X^3  0 X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0
 0  0  0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2  0 X^3  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3  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+28x^18+176x^19+516x^20+856x^21+989x^22+844x^23+470x^24+168x^25+26x^26+12x^28+5x^30+4x^31+1x^32

The gray image is a linear code over GF(2) with n=176, k=12 and d=72.
This code was found by Heurico 1.16 in 0.062 seconds.