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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+317x^32+1064x^34+489x^36+1888x^38+2592x^40+976x^42+528x^44+160x^46+162x^48+8x^50+6x^52+1x^68

The gray image is a code over GF(2) with n=156, k=13 and d=64.
This code was found by Heurico 1.16 in 79.8 seconds.