The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+101x^34+706x^35+1414x^36+2024x^37+2524x^38+2868x^39+2860x^40+1876x^41+1034x^42+628x^43+234x^44+64x^45+20x^46+20x^47+3x^48+4x^49+1x^50+2x^51

The gray image is a code over GF(2) with n=312, k=14 and d=136.
This code was found by Heurico 1.16 in 1.5 seconds.