The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+83x^26+88x^27+209x^28+336x^29+126x^30+88x^31+60x^32+31x^34+1x^36+1x^48

The gray image is a linear code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.031 seconds.