The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  0  0  1  1
 0  X  0  0  0  X  X  X  0  0  0  X  0  X  X  X  0  0  0  X  0  X  X  X  0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  X  0  X  X  X  0  0  0  X  0  X  X  X  0  0  X  X  0  X  X  0  X  X  X  X  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  0  X  X  0  0  0  X  X  0  0  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  X  X  0  0
 0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  0  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  0  X  X  0  X  0  X

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+14x^82+13x^84+2x^86+1x^88+1x^92

The gray image is a linear code over GF(2) with n=162, k=5 and d=82.
As d=82 is an upper bound for linear (162,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0928 seconds.