The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  X  1  1 X^2+X  1  1 X^3+X^2  1  1  1  1 X^3  1 X^3  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X X^2+X+1  1  X X+1  1 X^3+X^2 X^3+1  1 X^3 X^3+X^2+1 X^2+X X^3  1 X+1  1 X^3+X^2+1 X^2
 0  0 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3  0 X^2 X^3+X^2 X^3 X^2 X^2  0 X^2 X^3+X^2 X^3+X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3  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 21.

Homogenous weight enumerator: w(x)=1x^0+116x^21+215x^22+628x^23+154x^24+616x^25+195x^26+104x^27+4x^28+4x^29+5x^30+4x^31+1x^32+1x^34

The gray image is a linear code over GF(2) with n=192, k=11 and d=84.
This code was found by Heurico 1.16 in 0.031 seconds.