The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  X  2  2  0  1  1  X
 0  X  0  X  0  0  X X+2  2  2  X X+2 X+2 X+2  2  2  0  X  X  X  2  X  2  2  2  2  X X+2  2  0  2  0  X  X  X  X  2  0  2
 0  0  X  X  0 X+2  X  2  0  X  X  0  2  X  2 X+2  0 X+2  X  2  0  0  X  X X+2 X+2  X X+2  X X+2 X+2  X X+2 X+2 X+2 X+2  2  X  X
 0  0  0  2  0  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  0  2  0  2  2  0
 0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  2  0  0  2  0  0  2  2  2  2  0  0  0  0  0  2  2  2  0  0  2
 0  0  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  2  0  2  2  2  0  0  0  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+91x^34+24x^35+126x^36+64x^37+183x^38+80x^39+181x^40+64x^41+85x^42+24x^43+69x^44+21x^46+5x^48+4x^50+1x^52+1x^64

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 0.445 seconds.