The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2+2  1  1  1  1  X  X  1  1  X X^2+2 X^2  2
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2+2 X^2+X X^2+X X^2+2 X^2+2  X X^2+X+2  X X^2+X+2  X X^2+X+2 X^2+2 X+2 X+2  2 X^2+2 X^2+X+2  X  X  X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2  2  X X+2  X X^2+X+2 X^2  0 X^2+X X+2 X^2+X+2  2 X+2 X^2 X^2+2  0  0 X^2+X+2  2 X^2+X+2 X^2+2  2  X X+2
 0  0  0  2  2  2  0  2  0  2  2  0  0  2  0  2  2  0  0  0  2  0  2  0  2  2  2  0  0  2  0  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+312x^29+120x^30+612x^31+28x^32+608x^33+96x^34+184x^35+72x^37+8x^38+4x^39+2x^40+1x^48

The gray image is a code over GF(2) with n=256, k=11 and d=116.
This code was found by Heurico 1.16 in 94.8 seconds.