The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+225x^188+420x^189+600x^190+816x^191+1539x^192+1572x^193+1800x^194+1752x^195+2688x^196+2448x^197+2136x^198+2184x^199+3438x^200+3060x^201+3132x^202+2664x^203+3624x^204+3204x^205+2880x^206+2844x^207+3690x^208+3204x^209+2640x^210+2304x^211+2421x^212+2160x^213+1656x^214+936x^215+1518x^216+708x^217+492x^218+288x^219+273x^220+120x^221+24x^222+36x^223+30x^224+9x^228

The gray image is a code over GF(4) with n=272, k=8 and d=188.
This code was found by Heurico 1.16 in 19 seconds.