The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+16x^85+16x^86+32x^87+25x^88+8x^89+12x^90+4x^92+2x^94+1x^96+8x^97+2x^102+1x^120

The gray image is a code over GF(2) with n=176, k=7 and d=85.
This code was found by Heurico 1.16 in 0.223 seconds.