The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  0  1 X^2+X  1  1  1  1  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^2+X X+1  1 X^2+1  1 X^3+X^2 X^2+X X^3+X^2+X+1 X^2+1 X^3+X X^2+X
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 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+101x^20+64x^21+704x^22+576x^23+1212x^24+576x^25+704x^26+64x^27+82x^28+11x^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 0.063 seconds.