The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  2  0  2  2  2  0  2  2  2  0  2  2  0  2  2  2  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  2  2  0  2  2  2  0  2  2  2  2  2  2  0  2
 0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  0  0  2  0  2  0  0  2  2  0  0  2  2  2  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  0  2  2  0  2  2  2  0  2  0
 0  0  0  0  0  2  2  0  2  2  0  0  2  2  2  2  2  0  2  0  2  2  0  2  2  0  0  2  0  2  0  0  0  2

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+38x^32+440x^34+24x^36+8x^38+1x^64

The gray image is a code over GF(2) with n=272, k=9 and d=128.
This code was found by Heurico 1.16 in 0.141 seconds.