The generator matrix

 1  0  1  1  1 X^2+X  1  1  1 X^3+X^2  1 X^3+X  1  1  1  0  1  1  1 X^2+X  1  1  1  1 X^3+X^2  1  1 X^3+X^2 X^3+X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+1 X^3+X^2  1 X^3+X  1 X^2+1 X+1  0  1 X^3+X^2+X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+X^2+1 X^3+1 X^3+X^2  1 X^3+X^2 X^2+1  X  1
 0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0
 0  0  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 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+213x^26+192x^27+430x^28+384x^29+440x^30+192x^31+173x^32+18x^34+2x^36+2x^40+1x^42

The gray image is a linear code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 18 seconds.