The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X 1 1 X X 1 1 X X X^2 X 1 1 X X X^2 X X 1 X X^2 X^3 X^2 0 X X^2 X X^2 X^2 X^3 1 X^3 0 1 1
0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0
generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.
Homogenous weight enumerator: w(x)=1x^0+16x^62+8x^63+5x^64+2x^68
The gray image is a linear code over GF(2) with n=488, k=5 and d=248.
This code was found by Heurico 1.16 in 0.125 seconds.