The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+36x^61+140x^62+256x^63+437x^64+558x^65+838x^66+1142x^67+1326x^68+1640x^69+1958x^70+2170x^71+2534x^72+2872x^73+3244x^74+3624x^75+3851x^76+3972x^77+3890x^78+4020x^79+3896x^80+3686x^81+3455x^82+3148x^83+2849x^84+2342x^85+1864x^86+1456x^87+1182x^88+1010x^89+650x^90+476x^91+369x^92+232x^93+182x^94+80x^95+58x^96+32x^97+29x^98+10x^99+5x^100+2x^101+6x^102+2x^103+4x^104+2x^105

The gray image is a code over GF(2) with n=156, k=16 and d=61.
This code was found by Heurico 1.10 in 617 seconds.