The generator matrix

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

generates a code of length 68 over GR(16,4) who´s minimum homogenous weight is 187.

Homogenous weight enumerator: w(x)=1x^0+204x^187+468x^188+276x^189+372x^190+1560x^191+1473x^192+876x^193+1068x^194+2832x^195+2331x^196+1224x^197+1296x^198+4440x^199+3201x^200+1668x^201+1740x^202+5868x^203+4176x^204+1728x^205+1980x^206+5796x^207+3726x^208+1908x^209+1476x^210+4632x^211+2634x^212+1080x^213+984x^214+1824x^215+906x^216+348x^217+228x^218+480x^219+384x^220+108x^221+72x^222+12x^223+87x^224+18x^228+15x^232+18x^236+15x^240+3x^244

The gray image is a code over GF(4) with n=272, k=8 and d=187.
This code was found by Heurico 1.16 in 20.2 seconds.