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  X  0  X X^3+X^2  X  0  X X^3+X^2  X  0  X X^3+X^2  X X^3  X X^2  X  0  X X^3  X X^2  X X^2  X X^3  X X^2  X  X
 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^2 X^3+X  0 X^2+X X^3+X^2  X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^3+X^2+X  X  X  X X^2+X  X X^3+X^2+X  X  X  X  X  X X^3+X^2+X  X X^3+X  X X^3+X^2+X  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 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
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  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+16x^60+160x^61+156x^62+160x^63+15x^64+2x^66+2x^90

The gray image is a linear code over GF(2) with n=496, k=9 and d=240.
This code was found by Heurico 1.16 in 0.203 seconds.