The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+254x^29+910x^30+558x^31+936x^32+394x^33+644x^34+206x^35+118x^36+56x^37+14x^38+4x^39+1x^40

The gray image is a code over GF(2) with n=256, k=12 and d=116.
This code was found by Heurico 1.16 in 0.078 seconds.