The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2 X^2+X+2  1  1  1  1 X^2+X+2  1 X^2  1  X  1  1  1  1  X X^2+2 X^2  2 X+2  1 X^2+2  1  1  1  1  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3 X+2 X+1  1  2  1 X^2+X+3  1  X  3  0 X^2+X+1  1  1  1  1  1 X^2+X+2  1 X^2+X  1  2 X+3  2
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2 X^2+2 X^2+X+2 X^2+2 X^2+X+2 X^2  X X^2+2 X+2 X^2+X X^2+X+2 X^2+2 X^2+X X^2+X X^2+2  0  2 X^2+X+2 X+2 X^2+2  0 X^2+2 X^2+X+2 X^2+2 X+2 X^2+X 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+204x^36+340x^37+351x^38+314x^39+316x^40+336x^41+153x^42+2x^43+8x^44+16x^46+5x^48+1x^52+1x^56

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 0.063 seconds.