The generator matrix

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

generates a code of length 97 over Z4 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+94x^81+184x^82+286x^83+430x^84+568x^85+700x^86+896x^87+952x^88+1070x^89+1217x^90+1298x^91+1348x^92+1448x^93+1710x^94+1630x^95+1611x^96+1702x^97+1719x^98+1674x^99+1702x^100+1542x^101+1407x^102+1388x^103+1204x^104+1130x^105+955x^106+714x^107+599x^108+504x^109+360x^110+274x^111+200x^112+128x^113+61x^114+28x^115+16x^116+2x^117+7x^118+4x^119+4x^121+1x^172

The gray image is a code over GF(2) with n=194, k=15 and d=81.
This code was found by Heurico 1.10 in 185 seconds.