The generator matrix

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

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+156x^35+351x^36+614x^37+539x^38+832x^39+600x^40+536x^41+259x^42+126x^43+32x^44+30x^45+1x^46+4x^47+7x^48+4x^49+1x^50+2x^51+1x^52

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 19 seconds.