The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+523x^34+1528x^35+2350x^36+3876x^37+5211x^38+5748x^39+5258x^40+4264x^41+2217x^42+1044x^43+494x^44+148x^45+65x^46+28x^47+9x^48+4x^51

The gray image is a code over GF(2) with n=312, k=15 and d=136.
This code was found by Heurico 1.16 in 104 seconds.