The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+35x^38+48x^39+86x^40+48x^41+35x^42+1x^46+1x^50+1x^64

The gray image is a code over GF(2) with n=160, k=8 and d=76.
This code was found by Heurico 1.16 in 0.0205 seconds.