The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2  X  0  X X^2+2  X  X  X  2  X X^2  X  2  X  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X X^2+X  X X+2  X X^2+X  X X+2  X  0 X^2+2 X^2+X+2  X  X  X X^2+X+2  X  0 X^2+2
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  0  0  2  2  2  2  2  0  0  0  0  0  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+13x^32+72x^33+78x^34+80x^35+1x^36+8x^37+1x^38+1x^44+1x^46

The gray image is a code over GF(2) with n=272, k=8 and d=128.
This code was found by Heurico 1.16 in 0.032 seconds.