The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1 X^3+X^2  X  1  1  X  X
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X  0 X^3 X^3+X X^2+X X^3+X  X  0  0  X X^3+X X^2+X X^3+X^2 X^2+X X^2+X
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  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+88x^20+32x^21+272x^22+480x^23+309x^24+480x^25+272x^26+32x^27+73x^28+6x^32+3x^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 0.032 seconds.