The generator matrix

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

generates a code of length 26 over GR(16,4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+180x^68+312x^69+84x^70+480x^71+1131x^72+1236x^73+216x^74+960x^75+1704x^76+1476x^77+192x^78+1440x^79+2127x^80+1500x^81+168x^82+960x^83+1212x^84+852x^85+108x^86+21x^88+24x^92

The gray image is a code over GF(4) with n=104, k=7 and d=68.
This code was found by Heurico 1.16 in 0.39 seconds.