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  2  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  1  1  1  2  2
 0 12  0  4  0  0  4  4  8  8  4 12  0  8  4  4  0  8  4 12  0 12  8 12  0  8  4 12  0  0  4  4  4 12 12  4  0  8  8 12  8  4  4  0 12  0  4  0  4  8 12  8  8 12 12 12 12 12 12  0  0  0 12  4  4 12 12 12  4  8  8  0  4  0  4  8 12 12
 0  0 12  4  0 12 12  0  8  4  4  0  0  4 12  0  8  4  4  0  4  4  8  8  8  4  8 12  4  0  0 12  4  0  4  8  0 12 12  0  8  8  4  0  4 12 12 12 12  8 12  4 12  0  8 12 12  0  8  8 12  4  4  4  4 12  4 12 12  0 12 12 12  8  0 12  0  0
 0  0  0  8  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  8  0  0  8  8  8  0  8  8  0  8  0  0  0  8  8  0  0  0  0  8  8  0  8  8  0  8  8  8  0  8  8  0  0  0  0  0  8  8  8  8  0  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  8  0  8  0  8  0  0  0  8  8  0  0  8  8  0  8  0  8  0  8  8  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  8  0  0  0
 0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  0  0  8  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8  8  8  0  0  8  0  8  8  0  0  8  0  0  8  0  0  0  8  8  8  0  8  8  0  0  0  8  8  8  0  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+58x^72+115x^74+170x^76+1396x^78+166x^80+72x^82+36x^84+16x^86+10x^88+1x^90+6x^92+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 0.534 seconds.