The generator matrix

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

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+174x^34+372x^35+435x^36+512x^37+419x^38+520x^39+367x^40+416x^41+276x^42+256x^43+165x^44+76x^45+67x^46+20x^47+16x^48+4x^49

The gray image is a code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.11 in 0.169 seconds.