The generator matrix

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

generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+72x^68+48x^70+432x^71+195x^72+192x^73+288x^74+1104x^75+174x^76+576x^77+768x^78+2736x^79+144x^80+1344x^81+1248x^82+3312x^83+147x^84+960x^85+720x^86+1632x^87+87x^88+108x^92+69x^96+27x^100

The gray image is a code over GF(4) with n=108, k=7 and d=68.
This code was found by Heurico 1.16 in 0.489 seconds.