The generator matrix

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

generates a code of length 77 over Z4 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+78x^62+122x^63+303x^64+434x^65+617x^66+768x^67+769x^68+982x^69+1164x^70+1342x^71+1448x^72+1634x^73+1751x^74+1904x^75+1925x^76+1980x^77+2018x^78+1902x^79+1915x^80+1778x^81+1646x^82+1362x^83+1137x^84+966x^85+769x^86+602x^87+454x^88+358x^89+235x^90+172x^91+94x^92+56x^93+34x^94+16x^95+15x^96+4x^97+7x^98+2x^99+2x^100+1x^102+1x^124

The gray image is a code over GF(2) with n=154, k=15 and d=62.
This code was found by Heurico 1.10 in 129 seconds.