The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^2+X  1  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+1  1 X^2+X X^2+1  1  0 X+1  1 X^3+X X^3
 0  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3
 0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  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+40x^20+120x^21+264x^22+176x^23+259x^24+120x^25+40x^26+2x^28+2x^32

The gray image is a linear code over GF(2) with n=184, k=10 and d=80.
This code was found by Heurico 1.16 in -3.24e-008 seconds.