The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1  0  X
 0  X  0  X  0 X^3 X^2+X X^2 X^2+X X^2 X^2 X^3+X X^3+X^2+X X^2 X^3+X^2 X^2+X  X X^3+X^2 X^3 X^3+X^2  X X^3+X  X X^3+X^2+X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2 X^3  0  X X^3+X^2+X X^3+X  X X^3+X^2+X X^3+X^2 X^2 X^2+X X^3 X^3+X^2 X^2+X X^3+X^2+X  0 X^2
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0
 0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 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+154x^20+80x^21+620x^22+704x^23+1039x^24+672x^25+584x^26+64x^27+142x^28+16x^29+12x^30+7x^32+1x^40

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 0.187 seconds.