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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+7x^88+100x^89+6x^90+10x^93+1x^98+2x^101+1x^106

The gray image is a code over GF(2) with n=712, k=7 and d=352.
This code was found by Heurico 1.16 in 0.641 seconds.