The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  1 X^3+X^2  1  1  0  1  X  1
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^2+X X^3+X^2 X^2 X^3+X^2+X X^2+X  0 X^3  X X^3+X^2 X^3  0  X X^3+X^2 X^3+X^2  X  X X^3+X^2+X  0
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3  0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^2 X^2 X^3+X X^3+X^2 X^2+X  X X^2+X X^3+X^2+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+51x^26+164x^27+210x^28+216x^29+198x^30+112x^31+44x^32+8x^33+6x^34+12x^35+1x^40+1x^50

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 0.015 seconds.