The generator matrix

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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+218x^60+128x^61+364x^62+128x^63+146x^64+36x^66+2x^68+1x^112

The gray image is a linear code over GF(2) with n=496, k=10 and d=240.
This code was found by Heurico 1.16 in 0.281 seconds.