The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+76x^42+27x^44+20x^46+3x^48+1x^60

The gray image is a linear code over GF(2) with n=172, k=7 and d=84.
As d=85 is an upper bound for linear (172,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.0259 seconds.