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  2  1  1  1  1  1  1  1  1  4  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  1
 0  2 12  6  0  6 12 10  0 10 12  6  0  6 12 10  8 14  4 10  0 10  8  2 12  6 14 12  4  6  0 10  2  8 12  4  6 14  2  8  8  2  0 10 10  0  6 14  4  4  0  0  8  6  8  8  6  6 14 12 14  4  4  4 14 12  6 12 12  6  6  6  6  6  0 10
 0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  8  8  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  8  0  8  0  8  8  8  8  8  8  0  0  0  8  8  0  0  8  0  8  8  0  0  0  8  8  0  8  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  8  8  0  0  8  8  8  8  8  8  0  8  8  0  0  0  8  8  0  8  0  8  8  8  0  8  0  8  0  8  8  8  0  8  0  0  8  0  0  0  0  8  0
 0  0  0  0  8  0  0  0  8  0  0  0  0  8  0  8  8  8  0  8  0  8  8  0  0  8  8  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  8  0  8  8  0  8  8  8  0  8  0  0  0  8  0  8  8  0  8  8  0  8  0  0  8  8  8  8  0  8  8  0  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  8  0  8  0  8  0  8  8  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  0  8  8  8  0  8  0  0  0  8  0  8  0  0  8  8  8  8  0  8  0  8  0  0  8  0  0  0  0  8  0  0  8  0  0  8  8
 0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  8  8  0  0  0  8  0  8  8  0  8  0  0  0  8  0  8  8  0  0  8  8  0  8  0  8  0  0  8  8  8  0  0  0  0  0  8  0  0  8  8  8  0  0  8  8  0  0  0  8  8  8  8  0  8  8  8  0  8

generates a code of length 76 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+46x^69+173x^70+116x^71+156x^72+278x^73+161x^74+352x^75+1086x^76+1054x^77+172x^78+100x^79+127x^80+50x^81+126x^82+8x^83+34x^84+36x^85+7x^86+4x^88+8x^89+1x^138

The gray image is a code over GF(2) with n=608, k=12 and d=276.
This code was found by Heurico 1.16 in 84.2 seconds.