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

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

Homogenous weight enumerator: w(x)=1x^0+181x^80+180x^82+64x^83+432x^84+256x^85+776x^86+384x^87+839x^88+256x^89+324x^90+64x^91+176x^92+52x^94+66x^96+8x^98+21x^100+4x^102+9x^104+2x^108+1x^148

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 11 seconds.