The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X  1  1 X^2+2  1  1  1 X^2+2  1  1  0  0  1  1  1  1 X+2  X  2 X^2+2  1
 0  1  1 X^2 X+1  1  X  3  1  0  3  1 X^2+X+2 X^2+X+1  1 X^2+X X^2+X+1 X^2+2  1 X^2 X^2+1  1  1 X^2+1  X X^2+2 X^2+X+3  1  0  X X^2 X+3
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2 X^2+2 X^2+X  0 X^2  X X^2+X+2 X^2+X+2 X^2+X X^2+X+2  2 X^2+2  0  X X^2 X^2+2 X^2+2  0  2  0  X X^2+X+2  X X^2+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+126x^29+435x^30+368x^31+312x^32+346x^33+254x^34+106x^35+62x^36+8x^37+23x^38+6x^39+1x^40

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 0.031 seconds.