The generator matrix

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

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+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 0.016 seconds.