The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  1  X  1  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2  X X+2 X^2  0 X^2+X+2 X^2+2 X^2+X X^2  X X^2+X X+2 X^2  X X^2+2 X^2+X+2 X^2+2 X+2 X^2+2  2 X^2+X+2  0
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X+2  0  2 X+2 X^2+X X^2  0 X+2 X^2+X X+2 X^2 X^2+X+2 X^2+2 X^2+X  X  X X+2 X^2+2 X^2+X+2 X^2+2 X^2+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+70x^36+98x^37+213x^38+288x^39+195x^40+90x^41+43x^42+4x^43+21x^44+1x^72

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 0.032 seconds.