The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+34x^86+64x^87+47x^88+48x^89+19x^90+8x^91+9x^92+5x^94+3x^96+1x^98+1x^100+5x^102+8x^103+2x^108+1x^112

The gray image is a code over GF(2) with n=178, k=8 and d=86.
This code was found by Heurico 1.16 in 1.7 seconds.