The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+89x^18+76x^20+86x^22+1x^24+1x^26+2x^28

The gray image is a code over GF(2) with n=80, k=8 and d=36.
This code was found by Heurico 1.16 in 0.00378 seconds.