The generator matrix

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

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+12x^20+98x^21+20x^22+254x^23+17x^24+94x^25+11x^26+2x^27+2x^28+1x^42

The gray image is a linear code over GF(2) with n=184, k=9 and d=80.
This code was found by Heurico 1.16 in 0 seconds.