The generator matrix

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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+9x^82+34x^83+48x^84+36x^85+11x^86+16x^87+23x^88+12x^89+6x^90+12x^91+20x^92+12x^93+5x^94+3x^96+4x^97+2x^99+1x^104+1x^154

The gray image is a code over GF(2) with n=174, k=8 and d=82.
This code was found by Heurico 1.16 in 0.16 seconds.