The generator matrix

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

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+54x^18+32x^19+29x^20+10x^22+1x^24+1x^28

The gray image is a linear code over GF(2) with n=76, k=7 and d=36.
As d=36 is an upper bound for linear (76,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.00368 seconds.