The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^62+4x^64+4x^66+2x^68+2x^70+1x^72

The gray image is a code over GF(2) with n=496, k=7 and d=248.
This code was found by Heurico 1.16 in 0.125 seconds.