The generator matrix

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

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+106x^35+413x^36+564x^37+689x^38+712x^39+632x^40+480x^41+305x^42+90x^43+52x^44+16x^45+13x^46+12x^47+5x^48+4x^49+1x^50+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 0.156 seconds.