The generator matrix

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

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+72x^25+152x^26+174x^27+366x^28+542x^29+363x^30+170x^31+127x^32+56x^33+8x^34+6x^35+2x^36+2x^37+4x^38+2x^39+1x^46

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 0.25 seconds.