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
 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  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0  0 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 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  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  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X  0 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 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0  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  0  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0

generates a code of length 61 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+14x^58+48x^60+384x^61+48x^62+15x^64+2x^90

The gray image is a code over GF(2) with n=488, k=9 and d=232.
This code was found by Heurico 1.16 in 0.125 seconds.