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

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

Homogenous weight enumerator: w(x)=1x^0+22x^58+16x^59+40x^60+352x^61+40x^62+16x^63+23x^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 0.188 seconds.