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

generates a code of length 62 over Z4[X]/(X^2+2) 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 code over GF(2) with n=496, k=7 and d=244.
This code was found by Heurico 1.16 in 0.203 seconds.