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  X  1  1  X  1  1
 0  X  0  X  0  0  X  X X^2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X  2 X+2  2 X^2+X X^2  X X^2+2 X^2+X+2 X^2 X+2 X^2+X+2  0 X^2 X+2  2 X^2+2 X^2+X X^2+2
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2  X X^2+X  0  2 X^2+X+2 X^2  X X+2 X^2+X X^2+2  0 X^2+X+2 X^2+2 X^2+2  X X+2  X X^2+X+2 X^2 X^2+2 X^2 X^2+X X^2+2  2 X^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+246x^32+576x^34+176x^36+24x^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 94.6 seconds.