The generator matrix

 1  0  0  1  1  1 X^3+X^2+X  0  1 X^3+X  1 X^3  1  1  1  X  1  X X^2 X^3+X X^3+X^2 X^2  1  1
 0  1  0  1  X X^2+X+1  1  1 X^2  0 X^2+1  1 X^3+X+1 X^2+X X^2+X  0 X+1  1 X^3+X  1 X^2+X X^2 X^2 X^3
 0  0  1  1  1  0  1 X^3 X+1  1  X X^3+X^2+X+1 X^2+X+1 X^3+X^2+X X^3+X^2+X+1  1 X^3+X^2+1 X^3+X^2+X+1  1 X^2+1  1  1 X^3+X^2+1  0
 0  0  0  X X^3 X^3+X X^2+X  X  X X^3+X X^3+X^2 X^2 X^3 X^2+X X^2 X^3 X^3+X^2+X X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2 X^2+X X^2

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+64x^19+671x^20+1648x^21+3765x^22+6122x^23+8037x^24+6532x^25+3775x^26+1348x^27+601x^28+152x^29+43x^30+2x^31+2x^32+4x^33+1x^34

The gray image is a linear code over GF(2) with n=192, k=15 and d=76.
This code was found by Heurico 1.16 in 3.73 seconds.