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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+24x^61+78x^62+9x^64+8x^65+2x^66+6x^68

The gray image is a linear code over GF(2) with n=496, k=7 and d=244.
This code was found by Heurico 1.16 in 0.203 seconds.