The generator matrix

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

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+30x^20+146x^21+184x^22+498x^23+351x^24+500x^25+174x^26+124x^27+16x^28+10x^29+5x^30+2x^31+2x^32+4x^34+1x^38

The gray image is a linear code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.