The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X  1  0 X^3  X  1  X  X  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^2 X^2 X^2+X  X X^2+X X^3+X^2+X X^2+X  X  X X^3+X^2+X X^3 X^3  0 X^3
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3  0 X^2  0 X^3+X^2 X^2 X^3
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3 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+222x^20+96x^21+552x^22+672x^23+1062x^24+672x^25+500x^26+96x^27+178x^28+32x^30+9x^32+4x^34

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 2.7 seconds.