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  X  X  X  X  1  X  X  X  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2  X  1  1  1  1  1  1  1  1
 0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0  0 2X  0 2X 2X  0
 0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+28x^61+82x^62+6x^64+4x^66+4x^69+2x^70+1x^80

The gray image is a code over GF(2) with n=496, k=7 and d=244.
This code was found by Heurico 1.16 in 0.125 seconds.