The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  2  1  1  1  1  2  2  0  1  1  2  1  0  0  1  1  2  1  1  1  2  1  0  0  2  0  1  1  0  2  1  1  1  1  0  2  2  1  1  2  2  0  1  1  1  2  1  1  2  1  2  1  1  2  1  2  1  1  2  2  1  1  0  1  1  1  2  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  3  1  2  1  0  2  3  1  1  1  0  3  0  1  0  1  0  3  1  2  2  0  3  1  0  1  1  1  1  2  2  1  1  3  3  3  3  1  0  0  1  2  1  1  2  0  3  3  1  2  1  1  2  2  3  3  1  2  1  0  2  1  1  1  2  1  1  2  2  0  3  2  3  0
 0  0  1  1  1  0  1  0  1  1  0  2  1  3  3  2  0  3  2  3  1  3  2  3  3  2  1  0  0  1  1  0  1  1  1  3  1  2  2  0  1  2  3  2  2  1  3  1  1  1  1  3  3  0  1  0  3  2  3  0  2  2  2  1  3  0  0  1  1  0  2  3  1  3  1  3  3  3  0  1  0  1  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  0  0  2  2  2  0  2  0  0  0  0  2  2  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  2  2  0  2  2  0  0  0  2  0  0  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  0  0  0  2  2  0  0  2  0  2  2  0  2  0  2  0  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  2  2  0  0  0  2  2  2  0  2  2  0  0  0  2  0  0  2  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  0  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  2  2  2  0  2  2  2  0  0  2  0  2  2  2  2  0  2  2  2  2  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  0  0  2  0  0  2  0  2  2  2  0  2  2  2  0  2  2  2  2  0  2  2  2  0  0  2  2  2  0  0  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  0  0  2  2  2  2  0  0  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  0  0  2  0  0  2  0  2  2  0  2  2  2  2  0  2  2  0  2  2  0  0  2  0  0  0  0  0  2  2  2  0  0  2  0  2  2  2  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2  0  0  2  2  2  0  0  2  0  0  0  2  0  0  2  2  2  2  0  0  0  2  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  0  0  2  0  2  0  0  0  0  0  2  2  0  2  0  2  0  2  0  0  0  0  0  2  2  0  0  2  2  0  2  0  0  0  0  2  0  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+24x^70+46x^71+145x^72+144x^73+218x^74+238x^75+295x^76+308x^77+378x^78+376x^79+366x^80+434x^81+427x^82+476x^83+446x^84+518x^85+436x^86+462x^87+397x^88+388x^89+340x^90+326x^91+249x^92+192x^93+137x^94+108x^95+105x^96+58x^97+67x^98+16x^99+28x^100+6x^101+14x^102+8x^104+4x^106+6x^108+3x^110+2x^112

The gray image is a code over GF(2) with n=168, k=13 and d=70.
This code was found by Heurico 1.16 in 15.1 seconds.