The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^61+84x^62+176x^63+334x^64+446x^65+574x^66+688x^67+867x^68+958x^69+1094x^70+1318x^71+1415x^72+1606x^73+1778x^74+1968x^75+1923x^76+2024x^77+2122x^78+1892x^79+1801x^80+1740x^81+1609x^82+1318x^83+1121x^84+946x^85+734x^86+634x^87+463x^88+378x^89+280x^90+168x^91+115x^92+60x^93+38x^94+28x^95+16x^96+6x^97+7x^98+2x^99+4x^100+2x^104+2x^108

The gray image is a code over GF(2) with n=154, k=15 and d=61.
This code was found by Heurico 1.10 in 127 seconds.