The generator matrix

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

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+104x^20+128x^21+584x^22+768x^23+976x^24+768x^25+512x^26+128x^27+96x^28+24x^30+7x^32

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 0.062 seconds.