The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  0  1  1  1  2  1  X X+2  1  1  1  1  X  X  2  1  2  1  1  1  1  X  1  X  1  X  1
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  0  1 X+1  3  2  1  0  1  1 X+1  2  1  X  1  1  1  X  1  X X+3 X+2  1  2 X+2 X+2 X+2  X  0
 0  0  X  0  0  0  0  0  0  2  2  X  X  X  0 X+2  X X+2 X+2 X+2  2 X+2  0  2 X+2 X+2  X X+2  2 X+2  X X+2  0  X  2 X+2  2  0  X  0
 0  0  0  X  0  0  X  2  X  2 X+2  0  0  0 X+2 X+2 X+2 X+2  X  2  X  0  2  X  2 X+2  X  0 X+2 X+2  2  2  X  X  X  2  X  2  X  0
 0  0  0  0  X  0  0  X  2  2  0  2 X+2  X X+2  2 X+2  X  0  2 X+2 X+2 X+2  2  0  2  0  2  X X+2  2  X  X X+2  0  0  2  2 X+2  0
 0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  0  0  0  2  2  2  0  2  2  0  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+56x^32+98x^33+202x^34+338x^35+525x^36+724x^37+779x^38+912x^39+1015x^40+912x^41+774x^42+684x^43+485x^44+284x^45+158x^46+112x^47+56x^48+30x^49+36x^50+2x^51+6x^52+3x^54

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 2.2 seconds.