The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^53+134x^54+154x^55+202x^56+224x^57+218x^58+224x^59+265x^60+242x^61+249x^62+294x^63+242x^64+244x^65+210x^66+208x^67+205x^68+170x^69+150x^70+110x^71+78x^72+76x^73+52x^74+32x^75+25x^76+10x^77+11x^78+2x^79+5x^80+1x^84

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 2.49 seconds.