The generator matrix

 1  0  0  0  0  1  1  1  1  1  2  1  2  1  1 X+2  X X+2  1  2  0  1  1  2  X  0 X+2  1  2  0  1  1  1  X  X  1  1  0  1  1
 0  1  0  0  0  2  2  0  0  0  0  2  2  1  1  1  1  X X+1  1  X  1 X+3  1  X  1  1  3  X X+2  X  X X+3  X  1  0  0  1 X+3  0
 0  0  1  0  0  2  0  3 X+1 X+3  1  1  1 X+3 X+2 X+3  3  X X+2  1  1  0  1  1  0  2 X+2 X+3  1  1  2 X+2  1  1  2 X+3  X  3 X+1  2
 0  0  0  1  0  1  X  X X+2 X+1 X+1  3  1  1 X+3  2  3  1  0 X+3 X+2  0  0  2  1  1 X+3  3  1 X+2  3 X+2  1  3  0  3 X+1 X+1  3  2
 0  0  0  0  1  1 X+1  3  X X+1  X  X X+1 X+3 X+2  3  2 X+1  1 X+1  1  X X+2 X+2 X+2  X  2  1  3 X+3  2  2  0  0  1  2  2  0  2  0

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+65x^32+462x^33+850x^34+1316x^35+1994x^36+2584x^37+3090x^38+3804x^39+4244x^40+3886x^41+3448x^42+2602x^43+1856x^44+1312x^45+628x^46+336x^47+186x^48+72x^49+14x^50+6x^51+6x^52+4x^53+2x^54

The gray image is a code over GF(2) with n=160, k=15 and d=64.
This code was found by Heurico 1.13 in 8.44 seconds.