The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+28x^73+100x^74+174x^75+240x^76+286x^77+288x^78+342x^79+438x^80+410x^81+405x^82+416x^83+413x^84+464x^85+419x^86+408x^87+410x^88+396x^89+417x^90+384x^91+330x^92+280x^93+264x^94+224x^95+171x^96+148x^97+105x^98+90x^99+39x^100+34x^101+42x^102+10x^103+4x^104+2x^105+5x^106+2x^108+2x^110+1x^118

The gray image is a code over GF(2) with n=172, k=13 and d=73.
This code was found by Heurico 1.10 in 5.21 seconds.