The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+58x^76+92x^77+172x^78+246x^79+277x^80+320x^81+369x^82+408x^83+382x^84+416x^85+443x^86+390x^87+412x^88+426x^89+389x^90+434x^91+393x^92+398x^93+355x^94+338x^95+310x^96+264x^97+226x^98+156x^99+161x^100+96x^101+80x^102+66x^103+43x^104+30x^105+12x^106+10x^107+10x^108+6x^109+2x^110+1x^112

The gray image is a code over GF(2) with n=178, k=13 and d=76.
This code was found by Heurico 1.10 in 5.41 seconds.