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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+64x^72+78x^74+204x^76+512x^77+432x^78+512x^79+124x^80+36x^82+28x^84+16x^86+26x^88+14x^90+1x^144

The gray image is a code over GF(2) with n=624, k=11 and d=288.
This code was found by Heurico 1.16 in 0.55 seconds.