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

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+51x^58+16x^59+145x^60+608x^61+134x^62+16x^63+45x^64+7x^66+1x^116

The gray image is a code over GF(2) with n=488, k=10 and d=232.
This code was found by Heurico 1.16 in 6.28 seconds.