The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+44x^79+119x^80+108x^81+59x^82+82x^83+112x^84+80x^85+32x^86+58x^87+58x^88+32x^89+24x^90+34x^91+47x^92+18x^93+8x^94+16x^95+20x^96+8x^97+3x^98+18x^99+20x^100+4x^101+2x^103+2x^104+4x^105+2x^106+2x^107+5x^108+2x^109

The gray image is a code over GF(2) with n=172, k=10 and d=79.
This code was found by Heurico 1.16 in 0.547 seconds.