The generator matrix

 1  0  0  0  1  1  1  1  1  2  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  0  2  2 2a+3 2a+1  1 3a 3a+3 a+2 3a+3 2a+3  1 a+3 2a+2 2a+2  1 a+3 a+3 3a 3a+1 3a a+2  a  0
 0  0  1  0  1 3a+2 a+1  a 2a+2 3a+2 2a+3 3a+1  a a+2 3a+3 2a+1 2a+1 2a+2 2a+1  1  2 3a+1  0  3  2 a+1 2a+2  0
 0  0  0  1 3a+3  a  1  2 a+2 a+2  0  2 3a+1 2a+3 3a+3 a+1 3a 2a+1  a 2a+2 a+2 2a+3 3a+3 3a+1  1 2a+2 3a  0
 0  0  0  0  2  0 2a  0  0  0  2 2a  2  2 2a+2  2  0  2 2a 2a+2 2a+2 2a+2 2a+2 2a  0 2a 2a 2a

generates a code of length 28 over GR(16,4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+222x^68+228x^69+276x^70+780x^71+2052x^72+2196x^73+2412x^74+3132x^75+7005x^76+5832x^77+7200x^78+11160x^79+15378x^80+12840x^81+18120x^82+22872x^83+24270x^84+18612x^85+23940x^86+22620x^87+21612x^88+12996x^89+8844x^90+7020x^91+7128x^92+2592x^93+648x^94+69x^96+60x^100+24x^104+3x^108

The gray image is a code over GF(4) with n=112, k=9 and d=68.
This code was found by Heurico 1.16 in 83.8 seconds.