The generator matrix

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

generates a code of length 63 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+54x^53+112x^54+142x^55+206x^56+266x^57+216x^58+248x^59+285x^60+242x^61+257x^62+224x^63+247x^64+246x^65+226x^66+194x^67+160x^68+188x^69+160x^70+120x^71+96x^72+72x^73+46x^74+30x^75+27x^76+20x^77+7x^78+2x^79+2x^80

The gray image is a code over GF(2) with n=126, k=12 and d=53.
This code was found by Heurico 1.16 in 2.39 seconds.