The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  2  1 X+2  1  1  1  X  1  1  0  1  1  1  1  1  1  2  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1 X+2  1  3  3  X  1  0 X+1  1  0 X+2  0 X+2  2  X  2  2  0
 0  0  2  0  0  0  0  2  0  2  2  2  0  0  0  2  2  2  0  0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0
 0  0  0  2  0  0  2  2  0  2  0  2  0  2  2  2  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  2  0  0  0  2  0
 0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  0  2  0  2  2  2  0  0  0  0  0  2  2  2  0  0  0  0  2  0  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  0  2  2  0  2  0  2  0  2  2  0  2  0  2  2  2  0  2  2  0  0  0  0  0  0  0  0  2  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+54x^34+64x^35+105x^36+128x^37+121x^38+128x^39+93x^40+128x^41+67x^42+64x^43+51x^44+11x^46+4x^48+1x^50+2x^56+2x^58

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 0.0482 seconds.