The generator matrix

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

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+236x^26+716x^27+845x^28+828x^29+609x^30+428x^31+253x^32+132x^33+34x^34+8x^35+5x^36+1x^38

The gray image is a linear code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.16 in 0.063 seconds.