The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+242x^35+696x^36+1402x^37+1078x^38+1776x^39+907x^40+1072x^41+492x^42+310x^43+135x^44+54x^45+14x^46+8x^47+4x^48+1x^52

The gray image is a code over GF(2) with n=312, k=13 and d=140.
This code was found by Heurico 1.16 in 0.359 seconds.