The generator matrix

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

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+33x^24+60x^25+92x^26+310x^27+142x^28+826x^29+132x^30+294x^31+70x^32+16x^33+26x^34+18x^35+8x^36+10x^37+5x^38+2x^39+2x^40+1x^46

The gray image is a linear code over GF(2) with n=232, k=11 and d=96.
This code was found by Heurico 1.16 in 0.063 seconds.