The generator matrix

 1  0  0  1  1  1  0  1  1  2  0  X  1  1  1  1  1  1  1  X X+2  1  X X+2  1  1  0 X+2  0  1 X+2  2  1  1  1  X  2  2  0  2
 0  1  0  1  X X+3  1  0 X+2  1  1  2 X+1  1 X+2  2  1  3 X+2  X  1 X+3  1  1  2  1  1  1  1  1  1  1 X+1 X+2  2  2  1  2  1  1
 0  0  1  1  1  0 X+3  X X+3  X  1  1 X+3  X  1  1  0  0  0  1  2 X+3 X+1 X+1 X+2 X+2  3  X X+2 X+1  3  X  2 X+3 X+2  1  0  1  X  0
 0  0  0  X  0 X+2 X+2  X  X X+2  2 X+2  0  2  X  0  X  0  2  2  0 X+2 X+2  2  0 X+2 X+2  2  0  X  0  X X+2  X X+2  2  0 X+2 X+2  X
 0  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  2  2  2  0  2  0  0  2  0  0  0  2  2  0  0  0  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  0  2  2  2  0  0  2  2  2  2  0  0  2  2  2  2  2  0
 0  0  0  0  0  0  2  2  2  2  0  2  2  2  0  2  2  0  0  0  2  0  2  2  0  0  0  2  0  2  0  2  2  2  0  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+74x^32+172x^33+373x^34+682x^35+965x^36+1266x^37+1666x^38+2006x^39+2041x^40+1934x^41+1716x^42+1358x^43+929x^44+558x^45+305x^46+170x^47+80x^48+38x^49+34x^50+8x^51+6x^52+1x^54+1x^58

The gray image is a code over GF(2) with n=160, k=14 and d=64.
This code was found by Heurico 1.16 in 6.38 seconds.