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

generates a code of length 82 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+88x^74+4x^75+112x^76+36x^77+281x^78+208x^79+511x^80+520x^81+717x^82+516x^83+477x^84+212x^85+141x^86+40x^87+80x^88+59x^90+46x^92+18x^94+20x^96+8x^98+1x^132

The gray image is a code over GF(2) with n=656, k=12 and d=296.
This code was found by Heurico 1.16 in 1.06 seconds.