The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+30x^69+83x^70+158x^71+241x^72+274x^73+481x^74+532x^75+562x^76+628x^77+644x^78+704x^79+762x^80+860x^81+825x^82+898x^83+966x^84+944x^85+881x^86+884x^87+780x^88+760x^89+745x^90+588x^91+513x^92+432x^93+311x^94+260x^95+209x^96+136x^97+103x^98+62x^99+53x^100+30x^101+16x^102+10x^103+7x^104+2x^105+6x^106+1x^108+1x^110+1x^116

The gray image is a code over GF(2) with n=168, k=14 and d=69.
This code was found by Heurico 1.16 in 98.7 seconds.