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  2  1  1  2  2  1  2  1  1  1  1  2  1  1  2  1  1  2  1  1  1  1  1  2  1  1  2  1  2  1  1  1  2  1  2  1  2  1  1  1  2  1  1  2  2
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  8  0  8  8  0  0  8  0  0  8  8  0  0  8  8  0  8  0  0  8  8  0  0  8  0  8  8  8  8  8  0  8  0  8  8  8  0  0  8  8  8  8  8  8  8  0  8  8  8  8  0  0  0  8  8  8  8
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  0  8  0  0  8  0  8  8  0  8  8  0  0  0  8  8  0  8  0  0  8  0  0  8  0  8  0  8  8  8  0  0  8  0  0  8  8  0  8  0  8  8  0  8  8  8
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  0  0  8  8  8  8  8  8  0  8  0  8  8  0  8  0  0  8  0  8  0  0  0  0  8  0  8  0  0  0  0  0  0  0  8  8  8  0  8  8  0  8  8  0  0  0  8  0  8  8  0  8  0  0  0  8  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  0  0  0  0  0  8  8  0  0  0  8  8  8  0  8  8  0  8  8  8  8  0  8  8  8  8  8  0  0  0  0  0  8  8  0  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  8  0  0  0  8  0  0  0  8  8  0  8  8  0  8  8  8  8  0  8  8  8  0  0  0  0  8  8  8  0  0  8  8  0  8  8  8  8  0  0  8  0  8  0  0  0  0  0  8  0  8  8  0  8  8  8  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  8  0  0  8  8  0  8  8  8  0  8  8  8  0  0  0  0  8  8  0  8  8  0  0  8  0  0  8  8  0  8  0  0  0  8  8  8  0  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  8  0  0  0  0  0  0  0  8  8  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  0  8  8  8  0  8  0  8  8  8  0  8  8  0  8  0  0  8  0  8  0  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  8  0  8  8  0  8  0  8  0  0  0  0  0  8  0  0  0  8  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  0  8  0  8  0  0  8  0  0  8  8  8  8  0  8  0  8  0  8  8  8  8  8  0  0  0  0  0  0  0  0  0  8  8  0  8  8  8  0  8  0  0  0  0  8  8  0  0  0  8  8  8  0  8  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  8  8  8  8  0  8  0  8  8  8  0  8  0  8  0  8  0  0  8  8  8  0  8  8  8  8  8  8  0  8  8  8  0  0  0  8  0  8  8  8  8  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  0  0  0  0  8  8

generates a code of length 84 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+110x^72+2x^74+240x^76+76x^78+295x^80+196x^82+6477x^84+152x^86+269x^88+74x^90+121x^92+12x^94+88x^96+55x^100+20x^104+3x^108+1x^136

The gray image is a code over GF(2) with n=672, k=13 and d=288.
This code was found by Heurico 1.16 in 3.55 seconds.