The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1  1 X+2  1  1  1  0  X  1  2  0 X+2  X  X  X X+2  1  2  1 X+2  0  1  X  1  0 X+2  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  2  0 X+1  1 X+3  1  1 X+1  1 X+2 X+2  X X+2  1  1  1  1  3  X  1 X+2  X  3  1  1 X+1
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3 X+3  0  2  3  0 X+3 X+3 X+1  X  1  1  X  2  1 X+1  2  X  2  1  X X+3 X+2 X+2  1 X+1 X+1
 0  0  0  1  0  3  1  2  3  0 X+1  X  3 X+3  1  X X+2 X+3 X+1  X X+3  3 X+1 X+2  1  1 X+1  0  3 X+2  2  1  3  2  2 X+1  3  2 X+1
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3 X+1 X+2 X+1  3  1 X+3  2 X+2 X+2 X+1  X  1  2  2  X  3  1 X+3  3 X+2  1  2  X X+1  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+570x^32+612x^33+1618x^34+1388x^35+3394x^36+2492x^37+4584x^38+3228x^39+4826x^40+2640x^41+3362x^42+1400x^43+1604x^44+460x^45+398x^46+60x^47+99x^48+4x^49+20x^50+4x^51+2x^52+2x^54

The gray image is a code over GF(2) with n=156, k=15 and d=64.
This code was found by Heurico 1.13 in 969 seconds.