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

generates a code of length 75 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+180x^68+128x^70+32x^71+448x^72+256x^73+810x^74+448x^75+897x^76+256x^77+294x^78+32x^79+171x^80+26x^82+60x^84+18x^86+27x^88+4x^90+7x^92+1x^120

The gray image is a code over GF(2) with n=600, k=12 and d=272.
This code was found by Heurico 1.16 in 26.7 seconds.