The generator matrix

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

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+408x^36+608x^37+956x^38+656x^39+591x^40+344x^41+236x^42+96x^43+158x^44+24x^45+16x^46+2x^48

The gray image is a code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 0.094 seconds.