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 X X X X X X X 0 0 0 0 0 0 0 1 1 1 1 1 1 1 X X X X X 0 X X X 0 0 0 0 0 0
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 X X 0 X X X X X X 0 0 0 0 0 0 X 0 X X 0 0 X 0 X X X X 0 X X X 0 0 0
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 X X 0 X X 0 0 0 X X X X 0 0 0 X X X X 0 0 X X X X X 0 0 0 0 0 X X X 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 X X 0 0 0 X X 0 X X 0 0 X X 0 X X 0 0 X X X X 0 0 X X X 0 0 0 X 0 0 X X
generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 61.
Homogenous weight enumerator: w(x)=1x^0+16x^61+8x^62+7x^64
The gray image is a linear code over GF(2) with n=120, k=5 and d=61.
As d=61 is an upper bound for linear (120,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.067 seconds.