The generator matrix

 1  0  1  1  1  X  1  1 X^3+X^2+X  1  1 X^2+X  1  1  1 X^3+X^2+X  1 X^3  X X^3  1  1  1  1 X^3+X^2+X X^2  X  X  1
 0  1  1 X^2 X+1  1  X X^3+1  1  0 X^3+1  1 X^3+X^2+X X^2+X+1 X^3+X  1 X^2+X+1  1  1  1 X^3+X^2+1 X^2+X+1 X^3+X  0  1  1 X^2+X  1 X^3
 0  0  X X^3+X X^3 X^3+X X^3+X X^3 X^3+X^2+X X^3+X^2 X^2+X  0 X^2  X  0 X^3+X^2 X^2+X X^3+X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2 X^3+X^2+X X^2+X  X  X X^3+X X^2  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+122x^26+292x^27+531x^28+266x^29+464x^30+204x^31+111x^32+26x^33+5x^34+12x^35+12x^36+1x^38+1x^40

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 0.203 seconds.