The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+132x^28+112x^30+9x^32+2x^40

The gray image is a linear code over GF(2) with n=232, k=8 and d=112.
As d=115 is an upper bound for linear (232,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 0.015 seconds.