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 1 1 1 1 1
0 X 0 X^2+X 0 X^2+X 0 X 0 X^2+X 0 X 0 X^2+X 0 X X^2 X^2+X X^2 X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 X X^2 X^2 X
0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2
0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0
generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+31x^30+192x^31+31x^32+1x^62
The gray image is a linear code over GF(2) with n=124, k=8 and d=60.
As d=60 is an upper bound for linear (124,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.0123 seconds.