The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^62+16x^63+5x^64+6x^66+2x^68

The gray image is a linear code over GF(2) with n=496, k=6 and d=248.
This code was found by Heurico 1.16 in 0.156 seconds.