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

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+178x^32+448x^34+578x^36+192x^37+944x^38+832x^39+1829x^40+832x^41+1008x^42+192x^43+580x^44+368x^46+159x^48+48x^50+2x^52+1x^72

The gray image is a code over GF(2) with n=160, k=13 and d=64.
This code was found by Heurico 1.16 in 2.95 seconds.