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  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 X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X  0 X^3+X^2+X X^2  X X^3+X  0 X^3+X^2 X^2+X X^3 X^2+X X^3+X^2  X X^3+X  0 X^2+X X^3+X^2 X^2+X X^3 X^3+X^2 X^3+X X^3+X X^3 X^3 X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2+X X^2+X  0 X^2 X^3+X X^3+X^2+X X^3 X^2 X^3+X^2+X X^3+X  X X^3 X^3 X^3 X^3+X^2+X X^3+X  X X^3+X^2  X X^2  0  0
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3 X^2  0 X^3 X^3+X^2  0  0 X^3  0  0 X^3+X^2 X^2 X^3+X^2 X^3 X^2  0 X^3 X^2 X^3
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+7x^58+32x^59+120x^60+704x^61+120x^62+32x^63+7x^64+1x^122

The gray image is a linear code over GF(2) with n=488, k=10 and d=232.
This code was found by Heurico 1.16 in 0.281 seconds.