The generator matrix

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

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+212x^29+257x^30+390x^31+402x^32+360x^33+206x^34+148x^35+26x^36+36x^37+1x^38+6x^39+3x^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 56.5 seconds.