The generator matrix

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

generates a code of length 34 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+574x^32+384x^36+64x^40+1x^64

The gray image is a code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 0.031 seconds.