The generator matrix

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

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+53x^36+258x^37+96x^38+246x^39+81x^40+206x^41+47x^42+26x^43+8x^44+1x^50+1x^60

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.