The generator matrix

 1  0  0  1  1  1 3X+2  1  1  1  1  X 2X X+2 3X+2  1  1 2X+2  1  1  0  0  1  1  1  1  1 2X  1 X+2 X+2  1  1  1  1  2  X  1  0
 0  1  0  0 2X+3 3X+1  1 3X+2 2X+1  1  2  X 3X  1  1 3X+2 3X  1 3X+1 X+1  1 3X+2 2X  X X+3  1  0  1 2X+3 2X  1 2X+3  3 2X+2  X  1  1 X+1  1
 0  0  1  1  1 2X+2  1 2X+1 3X 3X+1 X+2  1  1 2X+3 3X  X  1  0 X+1  2 3X+3  1 X+1 3X+2  X  2 2X 3X+2 2X+1  1 X+3  X X+3 X+1  2 2X+2 3X+1 3X+3  3
 0  0  0  X 3X 2X 3X  X 2X+2 X+2  2 X+2 X+2  2 3X+2 3X+2  0 3X 2X+2 X+2  X 2X 3X 2X+2 X+2  X 2X+2  0 2X  0 X+2  0  2 X+2 3X 2X+2 2X 3X 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+411x^34+1304x^35+2734x^36+3940x^37+5130x^38+5602x^39+5797x^40+3724x^41+2321x^42+1116x^43+428x^44+156x^45+72x^46+26x^47+4x^49+2x^50

The gray image is a code over GF(2) with n=312, k=15 and d=136.
This code was found by Heurico 1.16 in 5.73 seconds.