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

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+103x^58+96x^59+136x^60+832x^61+64x^62+544x^63+31x^64+88x^66+64x^67+88x^68+1x^122

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.