The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+256x^37+229x^38+216x^39+109x^40+92x^41+42x^42+64x^43+1x^44+12x^45+1x^52+1x^54

The gray image is a code over GF(2) with n=312, k=10 and d=148.
This code was found by Heurico 1.16 in 11.7 seconds.