The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1 X^2  1  X  1  1  X  1  1  1  X
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2 X^3+X^2+X X^3+X^2  X  X  0 X^3+X^2 X^3 X^2 X^3+X^2+X  0 X^3+X^2+X X^2 X^2+X  X X^2
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2  X X^2 X^3+X  X X^3+X^2+X X^3+X  X X^2+X X^3+X X^3  0 X^2+X X^3 X^3 X^3+X^2+X X^3+X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^3  0 X^3+X^2  0 X^3 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 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+164x^25+317x^26+388x^27+707x^28+972x^29+773x^30+368x^31+181x^32+126x^33+61x^34+28x^35+7x^36+2x^41+1x^46

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 40.7 seconds.