The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+289x^20+416x^21+1038x^22+728x^23+940x^24+368x^25+252x^26+24x^27+25x^28+14x^30+1x^32

The gray image is a linear code over GF(2) with n=184, k=12 and d=80.
This code was found by Heurico 1.16 in 2.31 seconds.