The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^72+94x^73+152x^74+178x^75+212x^76+238x^77+222x^78+234x^79+248x^80+236x^81+223x^82+236x^83+191x^84+174x^85+185x^86+202x^87+171x^88+158x^89+129x^90+116x^91+91x^92+86x^93+87x^94+44x^95+54x^96+32x^97+20x^98+14x^99+6x^100+6x^101+6x^102+2x^104

The gray image is a code over GF(2) with n=166, k=12 and d=72.
This code was found by Heurico 1.10 in 1.08 seconds.