The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^18+18x^19+183x^20+12x^21+21x^22+2x^23+1x^34

The gray image is a code over GF(2) with n=160, k=8 and d=72.
This code was found by Heurico 1.16 in 0.016 seconds.