The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+23x^78+38x^79+64x^80+58x^81+48x^82+62x^83+29x^84+48x^85+28x^86+18x^87+17x^88+12x^89+17x^90+4x^91+9x^92+8x^93+7x^94+6x^96+2x^98+4x^99+2x^100+1x^106+2x^107+2x^110+2x^113

The gray image is a code over GF(2) with n=168, k=9 and d=78.
This code was found by Heurico 1.10 in 0.016 seconds.