The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  1  0  1  1  1  0  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X X^3+X^2 X^3+X X+1  1  0 X^3+X^2  0  X  0
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0 X^3
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  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+26x^18+48x^19+169x^20+412x^21+1022x^22+744x^23+1026x^24+416x^25+160x^26+40x^27+18x^28+4x^29+6x^30+1x^32+2x^34+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 0.062 seconds.