The generator matrix

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

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+70x^34+20x^35+168x^36+76x^37+190x^38+80x^39+152x^40+48x^41+86x^42+28x^43+47x^44+4x^45+34x^46+15x^48+4x^50+1x^60

The gray image is a code over GF(2) with n=156, k=10 and d=68.
This code was found by Heurico 1.16 in 0.0646 seconds.