The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+101x^58+272x^59+209x^60+336x^61+213x^62+336x^63+203x^64+272x^65+99x^66+2x^68+1x^70+1x^76+1x^78+1x^94

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 0.172 seconds.