The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+64x^81+68x^82+36x^83+74x^84+60x^85+41x^86+40x^87+27x^88+18x^89+9x^90+8x^91+7x^92+12x^93+7x^94+6x^95+10x^96+1x^98+2x^99+3x^100+2x^103+2x^104+6x^105+2x^106+2x^107+4x^108

The gray image is a code over GF(2) with n=172, k=9 and d=81.
This code was found by Heurico 1.13 in 10 seconds.