The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+110x^38+56x^39+47x^40+32x^41+2x^42+8x^43

The gray image is a code over GF(2) with n=312, k=8 and d=152.
This code was found by Heurico 1.16 in 1.05e-007 seconds.