The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  1  1  0 X^2+X  1  1  1  1  0 X^2+X  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X^2+X X+1 X^2+1  1  1 X^2+2 X+2 X^2+X+3 X^2+1  1  1  0 X^2+X X^2+2 X^2 X^2+X+2 X+1  2  0
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  2  2  0  0  2  2  0  0  2  0  2  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  0  2  2  0  0  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+64x^29+155x^30+240x^31+102x^32+240x^33+156x^34+64x^35+1x^46+1x^48

The gray image is a code over GF(2) with n=256, k=10 and d=116.
This code was found by Heurico 1.16 in 0.031 seconds.