The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+35x^34+200x^35+135x^36+736x^37+349x^38+1200x^39+345x^40+736x^41+118x^42+200x^43+29x^44+6x^46+2x^48+2x^50+1x^58+1x^62

The gray image is a code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.14 seconds.