The generator matrix

 1  0  1  1  1  X  1  1  2  1  1  0  1  1 X+2  1  1 X+2  0  1  1  2  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0 X+2  1
 0  1  1  2 X+1  1  X  3  1  0  1  1 X+2 X+3  1 X+2 X+3  1  0  2 X+1  1  X  3  1  2 X+2  0  X  2  0 X+2  X X+3  3 X+1  1  1  1 X+3
 0  0  X X+2  2 X+2  X  0  X  2 X+2  2  0  X  0  2 X+2  2  X  X  0 X+2 X+2  2  X  2 X+2 X+2  2  0  X  X  0  2 X+2 X+2  2 X+2 X+2  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+68x^39+61x^40+56x^41+19x^42+4x^43+9x^44+1x^46+1x^52+1x^58

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 0.0201 seconds.