The generator matrix

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

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+58x^25+169x^26+262x^27+372x^28+408x^29+326x^30+236x^31+119x^32+42x^33+26x^34+14x^35+4x^36+4x^37+6x^38+1x^42

The gray image is a linear code over GF(2) with n=232, k=11 and d=100.
This code was found by Heurico 1.16 in 0.047 seconds.