The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+252x^40+2x^48+1x^64

The gray image is a code over GF(2) with n=320, k=8 and d=160.
This code was found by Heurico 1.16 in 0.016 seconds.