The generator matrix

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

generates a code of length 83 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+69x^72+92x^73+150x^74+186x^75+223x^76+256x^77+197x^78+222x^79+247x^80+198x^81+204x^82+232x^83+188x^84+220x^85+195x^86+180x^87+155x^88+144x^89+130x^90+148x^91+133x^92+76x^93+84x^94+44x^95+28x^96+38x^97+23x^98+10x^99+12x^100+4x^102+2x^103+5x^106

The gray image is a code over GF(2) with n=166, k=12 and d=72.
This code was found by Heurico 1.16 in 3.03 seconds.