The generator matrix

 1  0  1  1  1 X^2+X+2  X  1  1 X^2+2  1  1  1  1  2 X^2+X+2  1  1  1  1 X^2+X  1 X+2  2  1  1 X^2  1  1  X  1  1  1  1  1  X  X  0  1
 0  1 X+1 X^2+X X^2+3  1  1  2 X^2+1  1 X^2+X+1 X^2+X+2 X^2+2 X+1  1  1  0 X+3  X  3  1 X^2+X  1  1  2  1  1 X^2 X^2+X+2  X X+2  1  1 X^2+X+3 X+1 X^2+X  1  1  0
 0  0 X^2  0 X^2+2 X^2 X^2+2 X^2  2  0 X^2+2 X^2  2  2 X^2 X^2+2  0 X^2+2 X^2  0  2  2  0 X^2+2 X^2+2 X^2 X^2+2 X^2 X^2+2 X^2  2 X^2  2  0  0  0 X^2+2  0  2
 0  0  0  2  0  0  2  0  2  2  2  2  2  0  0  2  0  2  0  2  2  0  0  2  2  2  0  0  2  0  2  0  0  2  0  0  0  0  2
 0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+42x^34+128x^35+419x^36+364x^37+900x^38+466x^39+876x^40+320x^41+393x^42+104x^43+43x^44+18x^45+6x^46+6x^47+1x^48+3x^50+4x^52+2x^53

The gray image is a code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.141 seconds.