The generator matrix

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

generates a code of length 20 over Z2[X]/(X^4) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+60x^19+132x^20+60x^21+1x^22+1x^26+1x^32

The gray image is a linear code over GF(2) with n=160, k=8 and d=76.
As d=78 is an upper bound for linear (160,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in -1.01e-007 seconds.