The generator matrix

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

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+49x^32+12x^34+2x^36

The gray image is a linear code over GF(2) with n=256, k=6 and d=128.
As d=128 is an upper bound for linear (256,6,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 6.
This code was found by Heurico 1.16 in 0.015 seconds.