The generator matrix

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

generates a code of length 68 over GR(16,4) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+75x^188+156x^190+216x^191+606x^192+252x^194+804x^195+1023x^196+336x^198+936x^199+1167x^200+696x^202+1296x^203+1317x^204+780x^206+1464x^207+1506x^208+540x^210+1044x^211+1035x^212+264x^214+360x^215+267x^216+48x^218+24x^219+57x^220+36x^224+21x^228+27x^232+15x^236+9x^244+3x^248+3x^256

The gray image is a code over GF(4) with n=272, k=7 and d=188.
This code was found by Heurico 1.16 in 1.53 seconds.