The generator matrix

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

generates a code of length 63 over Z4 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+96x^55+136x^56+112x^57+136x^58+142x^59+130x^60+142x^61+171x^62+148x^63+122x^64+96x^65+93x^66+98x^67+69x^68+52x^69+75x^70+62x^71+39x^72+32x^73+31x^74+24x^75+13x^76+14x^77+6x^78+6x^79+2x^80

The gray image is a code over GF(2) with n=126, k=11 and d=55.
This code was found by Heurico 1.16 in 29.2 seconds.