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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+30x^60+448x^62+31x^64+2x^92

The gray image is a code over GF(2) with n=496, k=9 and d=240.
This code was found by Heurico 1.16 in 0.14 seconds.