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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+61x^58+160x^59+306x^60+448x^61+258x^62+544x^63+28x^64+65x^66+128x^67+48x^68+1x^120

The gray image is a linear code over GF(2) with n=496, k=11 and d=232.
This code was found by Heurico 1.16 in 0.281 seconds.