The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  X  X  X  X  1 X^2  1  0 X^2  2  X  X  1 X^2  1 X^2  X  2  0  1  1
 0 X^2+2  2 X^2  0 X^2+2  2 X^2  0 X^2+2  2 X^2 X^2+2 X^2  0 X^2+2  2 X^2 X^2+2  0  2 X^2  0 X^2+2  2 X^2 X^2 X^2  0  2 X^2+2  2 X^2  0 X^2+2  2 X^2  0  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+18x^38+16x^39+9x^40+16x^41+2x^42+2x^44

The gray image is a code over GF(2) with n=312, k=6 and d=152.
This code was found by Heurico 1.16 in 0.031 seconds.