The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+30x^83+41x^84+54x^85+69x^86+50x^87+36x^88+40x^89+42x^90+22x^91+24x^92+22x^93+10x^94+20x^95+15x^96+6x^97+5x^98+2x^99+3x^100+4x^101+1x^102+4x^104+2x^105+2x^108+2x^111+1x^114+2x^115+2x^116

The gray image is a code over GF(2) with n=178, k=9 and d=83.
This code was found by Heurico 1.10 in 0.016 seconds.