The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  0  1  1 X^3+X^2+X X^3  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X+1  0  1 X^3+1 X^3+X^2+X  1  1 X^3 X^3+X^2+1 X^3+X^2+X+1 X^2+X  0 X^3+X^2+X X^2+X+1 X^2 X^3+X X^2  0
 0  0 X^2  0  0 X^3  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3  0 X^3  0 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3
 0  0  0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2  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+40x^20+228x^21+485x^22+802x^23+1011x^24+804x^25+469x^26+200x^27+30x^28+8x^29+4x^30+6x^31+6x^32+1x^34+1x^38

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 0.078 seconds.