The generator matrix

 1  0  0  1  1  1  2 X^2  0  1  1  1  X  1  1  1 X+2 X+2  1  1 X^2+X+2 X^2+X+2 X+2 X^2+2  1  1  1  2  2  1  1 X+2  1  1  1 X^2+2  1 X^2+X  1
 0  1  0  0 X^2+3 X^2+3  1  X  1 X^2+2  1 X^2+X+2  1 X+3 X^2+X+3  X X+2  1 X^2+1 X+2  1  1  2  1  1 X^2+1 X+2 X^2+X+2  1 X+3 X^2  1 X^2 X^2+X X+1  1 X+2 X+2  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+X X^2+X  X  1  3 X^2+X+1 X+2 X+1  1 X+1 X^2+3 X^2+2 X^2+2 X+2  1  1 X^2+X X+3 X^2+X+2  1  X X^2+2  1  X  3 X+3  X X^2+X+3 X+2  1  2
 0  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  0  2  0  2  0  2  2  0  0  0  0  0  2  2  2  0  0  0  0  2  2  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+216x^35+798x^36+1320x^37+1108x^38+1600x^39+1150x^40+980x^41+472x^42+324x^43+158x^44+36x^45+20x^46+4x^47+5x^48

The gray image is a code over GF(2) with n=312, k=13 and d=140.
This code was found by Heurico 1.16 in 0.344 seconds.