The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+121x^32+4x^36+2x^40

The gray image is a code over GF(2) with n=256, k=7 and d=128.
This code was found by Heurico 1.16 in 1.05e-007 seconds.