The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+150x^86+21x^88+52x^90+6x^92+6x^94+2x^96+16x^98+1x^100+1x^124

The gray image is a code over GF(2) with n=176, k=8 and d=86.
This code was found by Heurico 1.16 in 1.44 seconds.