The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  0 X^3+X  1  1  1  1  1  1  1  1  1  1  1  1 X^3  X X^3+X^2 X^2+X X^2 X^3+X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X X+1 X^3+1  1  1 X^3+X^2 X^3+X^2+X+1 X^2+1 X^3+X^2+X X^3+X X^3 X^2  X X^3+X+1  1 X^2+X+1 X^3+X^2+1  1  1  1  1  1  1  0 X^3 X^3+X^2+X X^3+X^2+X X^3 X^2+X X^3+X^2 X^3+X X^2 X^2  X X^2+X  0
 0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0

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+2x^58+344x^59+60x^60+208x^61+60x^62+344x^63+3x^64+2x^90

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 0.125 seconds.