The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^81+90x^82+58x^83+28x^84+40x^85+55x^86+44x^87+23x^88+16x^89+22x^90+14x^91+7x^92+2x^93+12x^94+2x^95+4x^96+8x^97+8x^98+2x^99+1x^100+2x^101+5x^102+2x^103+2x^107+4x^111

The gray image is a code over GF(2) with n=172, k=9 and d=81.
This code was found by Heurico 1.16 in 9.18 seconds.