The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+162x^70+403x^72+458x^74+526x^76+410x^78+421x^80+388x^82+392x^84+314x^86+251x^88+192x^90+90x^92+56x^94+18x^96+2x^98+8x^100+2x^102+2x^104

The gray image is a code over GF(2) with n=160, k=12 and d=70.
This code was found by Heurico 1.16 in 2.99 seconds.