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.