The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3  0 X^2 X^2 X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2  0 X^3
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^2  0 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2  0  0  0  0
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 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+22x^25+58x^26+62x^27+72x^28+616x^29+84x^30+44x^31+19x^32+14x^33+17x^34+6x^35+4x^36+4x^37+1x^50

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 0.015 seconds.