The generator matrix

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

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+32x^24+84x^25+308x^26+496x^27+688x^28+888x^29+690x^30+496x^31+297x^32+84x^33+20x^34+4x^36+2x^38+2x^40+4x^42

The gray image is a linear code over GF(2) with n=232, k=12 and d=96.
This code was found by Heurico 1.16 in 0.094 seconds.