The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  1  1  1  1  1  1  4  1  2  1  1  1  1  1  1  2  1  2  1  1  0  1  1  1  1  1  1  2  1  4  1
 0 12  0  0  0  8  0  8  0 12  4 12 12  4  4  4  4 12  0  0  8  0  4  0 12  8  4  8  4 12  4  8  8  0  4  4  8  0  4  0  4  4 12  4  8  0 12  0  0  4  4  8  8 12  4  0 12 12  8  4 12  0  0  0  0  8 12  8  8 12  4  0 12 12  8  4  0  4 12  4  8  0  8  4  4 12  0
 0  0 12  0  0  8  4 12  4  4  4 12  8 12  8  8  4  8  8  0  4 12  4  8  8  8  0  4 12  8 12  4  4  4  0  4  8  8  8  4  4 12  4  8  8 12  0  0  0  4 12  0 12  4  0  0  8  4 12  4  8 12  8  8  8 12  4  8  4  8  4  0  4  0  0  0  4 12  8  8  0  8  4  8 12  8 12
 0  0  0 12  0  4  4  4  8  0  4  0  8  4  4 12  0  4  8 12  8  8  8  4 12  0  0  4  4  8 12  4  0  0  8 12  4  8  0 12  4  0  0 12  4  4 12  4  8  8  4  4  8 12  8 12  8  4 12  0  0  4 12 12 12  4  8  0 12 12 12  0  8  8  4 12  4 12  0  0  0  4 12 12 12  4  8
 0  0  0  0 12  4  8 12 12  4  4  8  4  0  0 12  0  8  0  4  8  4  4  8  4 12  8  8  4 12  0  4  8  4  8 12  8  8 12  8  8  4  0  8 12 12  4 12  4  8  8  0  4  0 12  8  0  4  8  8  0  0 12  0  8  8  8  4 12  8  4 12 12  0  8  4  4 12 12  4  0 12  4  0  4 12 12

generates a code of length 87 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+210x^80+62x^82+422x^84+192x^85+884x^86+640x^87+966x^88+192x^89+176x^90+185x^92+28x^94+111x^96+2x^98+24x^100+1x^156

The gray image is a code over GF(2) with n=696, k=12 and d=320.
This code was found by Heurico 1.16 in 92.8 seconds.