The generator matrix

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

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+94x^36+88x^37+280x^38+144x^39+215x^40+88x^41+110x^42+2x^50+2x^56

The gray image is a code over GF(2) with n=312, k=10 and d=144.
This code was found by Heurico 1.16 in 0.031 seconds.