The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) 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 0.157 seconds.