The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+175x^70+466x^72+797x^74+1094x^76+1352x^78+1563x^80+1819x^82+1850x^84+1819x^86+1729x^88+1354x^90+1037x^92+647x^94+341x^96+184x^98+92x^100+38x^102+11x^104+5x^106+7x^108+1x^110+1x^112+1x^114

The gray image is a code over GF(2) with n=168, k=14 and d=70.
This code was found by Heurico 1.16 in 60.5 seconds.