The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+62x^25+274x^26+574x^27+789x^28+814x^29+700x^30+524x^31+253x^32+58x^33+22x^34+6x^35+5x^36+10x^37+4x^38

The gray image is a linear code over GF(2) with n=232, k=12 and d=100.
This code was found by Heurico 1.16 in 0.093 seconds.