The generator matrix

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

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+57x^26+140x^27+262x^28+104x^29+261x^30+140x^31+57x^32+1x^42+1x^46

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 0.016 seconds.