The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) 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.