The generator matrix

 1  0  0  0  1  1  1  1 X^3+X  1  X X^3  1  1  0  1  1  1 X^2 X^2+X  0  1  1  1
 0  1  0  0  0 X^3 X^2+1 X^3+X+1  1 X^3+1  1 X^3+X X^2+X+1 X^3+X^2  1 X^3+1  0 X^3+X+1 X^2+X  X  X X^3+X^2+X X^3+X^2+X+1 X+1
 0  0  1  0  1 X^3+X^2+X X^2  X  X  1 X^2+1  1 X^3+X+1 X+1 X+1  X X^3 X^3+X^2 X^3+X  1  1 X^2+X X^3+X^2+1 X^2+X
 0  0  0  1  1 X+1 X^2+X+1 X^3 X+1  X X^3+1 X^2+X+1 X^2+1 X^2+X X^3 X^3+X^2 X+1 X^3+1  1 X^3+X^2+1 X^3+X  1 X^2+X+1 X^2+X
 0  0  0  0 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 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 19.

Homogenous weight enumerator: w(x)=1x^0+618x^19+2303x^20+6606x^21+15002x^22+24702x^23+31889x^24+25782x^25+15232x^26+6118x^27+2025x^28+666x^29+98x^30+18x^31+6x^32+2x^33+4x^34

The gray image is a linear code over GF(2) with n=192, k=17 and d=76.
This code was found by Heurico 1.16 in 189 seconds.