The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+340x^34+838x^36+998x^38+805x^40+712x^42+297x^44+78x^46+10x^48+16x^50+1x^52

The gray image is a code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.16 in 4.22 seconds.