The generator matrix

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

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+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.