The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+108x^24+944x^25+1944x^26+4250x^27+5490x^28+7350x^29+5479x^30+4458x^31+1695x^32+696x^33+246x^34+90x^35+10x^36+2x^37+3x^38+2x^39

The gray image is a linear code over GF(2) with n=232, k=15 and d=96.
This code was found by Heurico 1.16 in 4.52 seconds.