The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+406x^36+714x^37+736x^38+844x^39+461x^40+350x^41+274x^42+152x^43+131x^44+20x^45+5x^46+1x^48+1x^50

The gray image is a code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 0.11 seconds.