The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+14x^18+32x^19+15x^20+1x^26+1x^30

The gray image is a linear code over GF(2) with n=76, k=6 and d=36.
As d=37 is an upper bound for linear (76,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.000916 seconds.