The generator matrix

 1  0  1  1  1 X^3 X^2+X  1  1  1 X^3+X^2+X  1  1  1  1  1  X  1 X^2  1  X  1  1  1  1  1  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1  1 X^3 X^3+X^2+1 X^2+X  1 X^3+1 X^2+X+1 X+1 X^3+X^2+X+1 X^3+X^2+1 X^3+X X^2  1  X  1 X^3+1 X^3+1 X^3+X+1 X^3+X+1 X^2+1  0 X^3+X^2+X+1  0
 0  0 X^2 X^3+X^2 X^3 X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2  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 X^3+X^2 X^3  0 X^3+X^2 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+36x^26+136x^27+280x^28+200x^29+216x^30+88x^31+18x^32+24x^33+20x^34+3x^36+1x^40+1x^44

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 0.172 seconds.