The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+409x^16+624x^18+664x^20+272x^22+78x^24

The gray image is a linear code over GF(2) with n=76, k=11 and d=32.
As d=32 is an upper bound for linear (76,11,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 11.
This code was found by Heurico 1.11 in 32.7 seconds.