The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+130x^35+397x^36+554x^37+703x^38+702x^39+669x^40+428x^41+250x^42+130x^43+77x^44+34x^45+6x^46+6x^47+8x^48+1x^54

The gray image is a code over GF(2) with n=312, k=12 and d=140.
This code was found by Heurico 1.16 in 0.156 seconds.