The generator matrix

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

generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+528x^69+756x^70+408x^71+570x^72+2148x^73+2172x^74+2052x^75+1371x^76+4476x^77+4716x^78+3780x^79+2901x^80+7284x^81+6732x^82+5388x^83+3072x^84+6852x^85+4848x^86+2196x^87+756x^88+1752x^89+744x^90+15x^92+12x^96+6x^100

The gray image is a code over GF(4) with n=108, k=8 and d=69.
This code was found by Heurico 1.16 in 5.91 seconds.