The generator matrix

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

generates a code of length 73 over Z4 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+179x^58+372x^59+514x^60+724x^61+1022x^62+1228x^63+1651x^64+1748x^65+2113x^66+2632x^67+2967x^68+3250x^69+3838x^70+3994x^71+4010x^72+4386x^73+4056x^74+4180x^75+3886x^76+3518x^77+3170x^78+2654x^79+2361x^80+1966x^81+1486x^82+1012x^83+751x^84+570x^85+427x^86+266x^87+222x^88+130x^89+77x^90+44x^91+18x^92+18x^93+14x^94+2x^95+2x^96+2x^97+1x^98+1x^102+1x^112

The gray image is a code over GF(2) with n=146, k=16 and d=57.
This code was found by Heurico 1.10 in 310 seconds.