The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^38+44x^39+7x^40+4x^43+2x^50

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 0.015 seconds.