The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+222x^35+793x^36+1210x^37+1365x^38+1376x^39+1300x^40+862x^41+535x^42+300x^43+145x^44+56x^45+19x^46+6x^47+1x^48+1x^50

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 0.375 seconds.