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  1  1  X  1  1  X  1
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2  2 X^2  2 X^2+2  2 X^2  2 X^2  2 X^2  0 X^2+2  2 X^2  2 X^2  2 X^2  0 X^2+2 X^2+2  0 X^2+2 X^2+2  0
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  0  2  0  0  0  0  0  2  2  0  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  0  2  2  0  2  2  2  0  0  2  0  2  0  0  0  2  2  0  2  0  0  2  2  0  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+18x^36+32x^37+13x^38+384x^39+13x^40+32x^41+17x^42+1x^46+1x^74

The gray image is a code over GF(2) with n=312, k=9 and d=144.
This code was found by Heurico 1.16 in 0.047 seconds.