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

generates a code of length 64 over GR(16,4) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+306x^176+864x^177+324x^178+180x^179+1533x^180+2688x^181+984x^182+396x^183+2307x^184+4728x^185+1392x^186+456x^187+3390x^188+6180x^189+1776x^190+468x^191+3849x^192+7284x^193+1908x^194+852x^195+4200x^196+6840x^197+1704x^198+516x^199+2523x^200+3888x^201+888x^202+144x^203+1035x^204+1188x^205+240x^206+60x^207+192x^208+132x^209+45x^212+30x^216+21x^220+18x^224+6x^232

The gray image is a code over GF(4) with n=256, k=8 and d=176.
This code was found by Heurico 1.16 in 21.9 seconds.