The generator matrix

 1  0  1  1  1 X^2+X  1  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1  1  1  0  1 X^2+X  X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+1 X^3+X^2  1 X^3+X  1 X^2+1 X+1 X^3+X^2+X+1 X^3+1 X^3+X^2+X+1 X^3+1  0  1 X^3+X^2  1  0
 0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0 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+174x^20+128x^21+576x^22+256x^23+641x^24+128x^25+128x^26+13x^28+2x^32+1x^36

The gray image is a linear code over GF(2) with n=184, k=11 and d=80.
This code was found by Heurico 1.16 in 0.032 seconds.