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

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+144x^32+310x^34+64x^35+501x^36+256x^37+614x^38+384x^39+626x^40+256x^41+426x^42+64x^43+267x^44+114x^46+53x^48+8x^50+7x^52+1x^60

The gray image is a code over GF(2) with n=156, k=12 and d=64.
This code was found by Heurico 1.16 in 0.957 seconds.