The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  2  1  1 X+2  1  1  X  1  1  0  1  1  0  1  1  1  1  X  1  1
 0  1 X+1 X+2  1  1  0 X+1  1  3 X+2  1  0 X+1  1 X+2  3  1  2 X+3  1 X+2  3  1  X  3  1  0 X+2  X X+2 X+1  1  2 X+1  3  0  0  3  1
 0  0  2  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  2  0  2  0  2  2  0  2  2  0  0  0  2  0  0  2  0  2  2
 0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  2  0  0  2  0  0  0  2
 0  0  0  0  2  0  2  2  0  0  2  0  0  2  2  0  2  2  2  0  2  2  0  2  2  0  0  2  0  0  0  2  2  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  0  2  0  0  2  2  2  0  0  2  0  2  2  0  2  0  2  2  2  2  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+198x^36+176x^38+289x^40+192x^42+135x^44+16x^46+13x^48+2x^52+1x^56+1x^60

The gray image is a code over GF(2) with n=160, k=10 and d=72.
This code was found by Heurico 1.16 in 4.68 seconds.