The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1  X X^2 X^2
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3  0 X^2 X^2 X^2  0 X^2 X^3+X^2  0 X^3
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3  0 X^2 X^2  0  0 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^2 X^3 X^3  0 X^3+X^2 X^2
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  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+38x^25+39x^26+120x^27+95x^28+464x^29+86x^30+116x^31+24x^32+18x^33+3x^34+4x^35+7x^36+8x^37+1x^48

The gray image is a linear code over GF(2) with n=232, k=10 and d=100.
This code was found by Heurico 1.16 in 0.031 seconds.