The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+38x^78+28x^79+93x^80+90x^81+111x^82+108x^83+106x^84+120x^85+102x^86+120x^87+104x^88+92x^89+102x^90+120x^91+82x^92+120x^93+73x^94+108x^95+73x^96+90x^97+59x^98+28x^99+24x^100+5x^102+12x^104+13x^106+10x^108+5x^110+5x^112+2x^114+2x^116+1x^118+1x^122

The gray image is a code over GF(2) with n=178, k=11 and d=78.
This code was found by Heurico 1.16 in 1.18 seconds.