The generator matrix

 1  0  0  0  0  0  1  1  1  2  1  1  1  1  1  2  1  1  1  0  2  2  1  2  0  2  1  2  0  2  1  1  2  1  1  0  0  1  1  2  2  1  0  2  1  1  2  1  0  0  2  1  0  0  1  1  1  0  1  2  1  2
 0  1  0  0  0  0  0  0  0  0  0  1  2  2  1  1  3  1  1  1  1  2  1  1  0  1  2  1  2  0  1  1  1  3  3  1  0  0  1  1  1  2  2  1  2  0  0  3  2  2  2  3  1  1  3  3  2  1  1  0  3  1
 0  0  1  0  0  0  0  0  0  0  1  0  3  3  3  1  1  2  2  0  1  0  3  2  1  3  1  2  1  1  3  1  2  2  1  0  2  3  0  3  1  0  2  1  1  1  1  0  1  1  1  1  2  3  2  2  0  0  0  1  3  0
 0  0  0  1  0  0  0  1  1  1  3  3  1  0  0  1  3  2  1  0  3  2  2  3  3  0  0  3  2  2  2  1  1  3  3  0  1  3  3  3  0  0  0  1  2  0  3  2  1  3  2  0  1  0  1  0  3  0  1  3  3  1
 0  0  0  0  1  0  1  1  0  3  2  2  1  3  2  2  3  3  1  3  3  2  3  0  0  1  0  1  3  2  1  0  3  3  1  1  1  0  0  0  2  1  1  1  3  2  1  3  0  2  1  2  0  1  3  2  2  1  0  3  3  3
 0  0  0  0  0  1  1  2  3  1  0  2  1  2  0  2  2  0  3  3  1  1  1  1  3  2  1  0  3  2  3  1  2  3  2  1  2  0  3  1  0  0  0  1  1  2  1  1  2  3  0  1  0  2  0  1  2  1  1  0  3  1
 0  0  0  0  0  0  2  0  2  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  2  0  0  2  0  2  0  2  2  0  0  2  2  2  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  2

generates a code of length 62 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+104x^51+175x^52+230x^53+295x^54+318x^55+403x^56+450x^57+424x^58+382x^59+500x^60+528x^61+517x^62+578x^63+493x^64+476x^65+520x^66+424x^67+327x^68+278x^69+230x^70+206x^71+116x^72+82x^73+56x^74+34x^75+30x^76+4x^77+5x^78+2x^79+2x^80+1x^86+1x^88

The gray image is a code over GF(2) with n=124, k=13 and d=51.
This code was found by Heurico 1.16 in 9.44 seconds.