The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) 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.