The generator matrix
1 0 0 0 1 1 1 1 1 X 1 X 1 1 0 X 0 X 1 0 1 1 1 X 1 0 0 1 1
0 1 0 0 0 1 X 0 X+1 1 1 1 X 0 X 1 1 0 X+1 1 X 0 X+1 1 1 1 1 X+1 0
0 0 1 0 1 1 1 X 0 1 X 0 X+1 X X X 1 1 X X+1 1 X X 0 1 X 1 0 X
0 0 0 1 1 0 0 1 X X X+1 1 X X+1 1 X X 1 X+1 X+1 X 0 0 1 X 0 X+1 X 0
0 0 0 0 X 0 0 0 0 0 0 X X X 0 0 X X X 0 X X 0 0 X X 0 0 X
0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 0 X X 0
generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+187x^24+136x^26+240x^28+128x^30+169x^32+104x^34+40x^36+16x^38+3x^40
The gray image is a linear code over GF(2) with n=58, k=10 and d=24.
As d=24 is an upper bound for linear (58,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.0807 seconds.