The generator matrix

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

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+36x^38+40x^39+39x^40+8x^41+3x^42+1x^50

The gray image is a code over GF(2) with n=312, k=7 and d=152.
This code was found by Heurico 1.16 in 0.031 seconds.