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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+103x^58+96x^59+136x^60+832x^61+64x^62+544x^63+31x^64+88x^66+64x^67+88x^68+1x^122

The gray image is a code over GF(2) with n=496, k=11 and d=232.
This code was found by Heurico 1.16 in 0.281 seconds.