The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+102x^82+203x^84+178x^86+136x^88+102x^90+78x^92+64x^94+42x^96+20x^98+36x^100+28x^102+7x^104+16x^106+7x^108+2x^110+2x^112

The gray image is a code over GF(2) with n=178, k=10 and d=82.
This code was found by Heurico 1.16 in 0.322 seconds.