The generator matrix
1 0 0 1 1 1 X 1 1 X 1 X 1 0 1 1 1 1 1 1 0 1 1 0 1 X X 0 0 1 1 X 1
0 1 0 0 1 X+1 1 X X+1 1 0 0 1 1 X X X 0 X X+1 1 0 1 X X+1 X 1 1 0 X 1 1 0
0 0 1 1 X+1 0 X+1 1 X+1 X X 1 X 1 1 X+1 X+1 1 X X X X+1 1 1 1 1 1 X+1 0 0 0 0 X+1
0 0 0 X X X 0 0 0 X X X 0 X X 0 X 0 0 X 0 0 X X X X 0 0 X 0 X 0 0
generates a code of length 33 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.
Homogenous weight enumerator: w(x)=1x^0+108x^32+18x^40+1x^48
The gray image is a linear code over GF(2) with n=66, k=7 and d=32.
As d=32 is an upper bound for linear (66,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 20.6 seconds.