The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+32x^80+88x^82+69x^84+24x^86+17x^88+6x^90+2x^92+12x^96+2x^98+3x^100

The gray image is a code over GF(2) with n=168, k=8 and d=80.
This code was found by Heurico 1.10 in 0.016 seconds.