The generator matrix

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

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+128x^20+232x^21+414x^22+844x^23+1013x^24+716x^25+344x^26+228x^27+115x^28+28x^29+26x^30+6x^32+1x^36

The gray image is a linear code over GF(2) with n=192, k=12 and d=80.
This code was found by Heurico 1.16 in 0.094 seconds.