The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1 X^3+X^2+X  0 X^3  1 X^3+X^2+X X^2+X  1  1  1  1  1  1  1
 0  1  0  0 X^2 X^3+1  1  1 X^2+1 X^3+1 X^3+X^2+X  1 X^2+X  1 X^3+X  1 X^3+X^2 X^3+X^2+X+1  X X^2+1  0 X^3+X+1 X^3+X^2  0
 0  0  1  0 X^2+1  1 X^2 X^2+1 X+1 X^2+X  0 X^3+X  1 X+1 X^3+X^2+1 X^2+1 X^2 X+1 X^2+X+1 X^2+1 X^3+X^2+X  X X^3+X^2+1  0
 0  0  0  1  1 X^2 X^2+1 X^3+1 X+1 X^2+X X^3+1 X^3+1 X^3+X+1 X^2  X X^2+X+1  1 X^3+X+1  0 X^3+X+1 X^2+1 X^3+X^2+X+1 X^3+X^2+X+1 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+248x^19+1148x^20+3384x^21+7418x^22+12854x^23+15269x^24+13174x^25+7434x^26+3212x^27+1058x^28+268x^29+50x^30+6x^31+4x^32+6x^33+2x^34

The gray image is a linear code over GF(2) with n=192, k=16 and d=76.
This code was found by Heurico 1.16 in 13.5 seconds.