The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  X  1 X^2  1  X  1  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3 X^3 X^2  0 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^3 X^2 X^2 X^3  0 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^2 X^2  0 X^2 X^3 X^3+X^2 X^3 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  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+141x^20+24x^21+154x^22+360x^23+732x^24+360x^25+126x^26+24x^27+74x^28+38x^30+11x^32+2x^34+1x^36

The gray image is a linear code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.047 seconds.