The generator matrix

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

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+272x^38+59x^40+128x^42+48x^46+3x^48+1x^56

The gray image is a code over GF(2) with n=160, k=9 and d=76.
This code was found by Heurico 1.16 in 74.8 seconds.