The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2 X^2+2 X^2+2 X^2+2 X^2  0  2  0  2  0  2 X^2+2 X^2 X^2  0 X^2  2  0  0
 0  0  2  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  2  2  0  0  0  2  2  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+15x^32+222x^34+16x^36+2x^50

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 0.016 seconds.