The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+180x^74+377x^76+522x^78+464x^80+460x^82+406x^84+412x^86+318x^88+292x^90+251x^92+182x^94+121x^96+52x^98+46x^100+12x^102

The gray image is a code over GF(2) with n=168, k=12 and d=74.
This code was found by Heurico 1.16 in 4.84 seconds.