The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+40x^18+120x^19+184x^20+386x^21+806x^22+1046x^23+809x^24+380x^25+164x^26+108x^27+23x^28+2x^29+14x^30+6x^31+6x^32+1x^36

The gray image is a linear code over GF(2) with n=184, k=12 and d=72.
This code was found by Heurico 1.16 in 0.109 seconds.