The generator matrix

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

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+46x^37+136x^38+166x^39+103x^40+42x^41+15x^42+2x^43+1x^66

The gray image is a code over GF(2) with n=312, k=9 and d=148.
This code was found by Heurico 1.16 in 0.031 seconds.