The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+364x^36+776x^37+833x^38+612x^39+541x^40+440x^41+236x^42+132x^43+128x^44+24x^45+3x^46+6x^48

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 0.109 seconds.