The generator matrix

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

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+112x^34+652x^35+1377x^36+2028x^37+2708x^38+2906x^39+2683x^40+2010x^41+952x^42+488x^43+315x^44+88x^45+36x^46+18x^47+8x^48+2x^49

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 1.48 seconds.