The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) 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 11.8 seconds.