The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X X X^2 X^2 X^2 1 X 1 1 1 X^2 X X X
0 2 0 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 0 2 2 0 0 2 0
0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 0 2 2 0 0 2 2 0
generates a code of length 35 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+6x^34+44x^35+6x^36+4x^39+1x^40+2x^42
The gray image is a code over GF(2) with n=280, k=6 and d=136.
This code was found by Heurico 1.16 in 0.016 seconds.