The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  X  X  X  X
 0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2
 0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  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+18x^18+32x^19+6x^20+4x^22+1x^24+2x^26

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 0.00264 seconds.