The generator matrix

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

generates a code of length 77 over Z4 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+90x^61+260x^62+390x^63+612x^64+786x^65+1036x^66+1356x^67+1565x^68+1958x^69+2174x^70+2508x^71+2898x^72+3346x^73+3517x^74+3750x^75+4113x^76+4120x^77+4232x^78+3830x^79+3804x^80+3576x^81+3125x^82+2798x^83+2276x^84+1954x^85+1474x^86+1144x^87+875x^88+650x^89+447x^90+298x^91+205x^92+130x^93+96x^94+48x^95+33x^96+26x^97+19x^98+6x^99+1x^100+4x^101+4x^102+1x^104

The gray image is a code over GF(2) with n=154, k=16 and d=61.
This code was found by Heurico 1.10 in 590 seconds.