The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+440x^36+256x^38+708x^40+256x^42+340x^44+33x^48+12x^52+2x^56

The gray image is a code over GF(2) with n=160, k=11 and d=72.
This code was found by Heurico 1.16 in 2.42 seconds.