The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1
 0  2  0  0  0  2  2  2 2a  0  2 2a 2a 2a 2a  2 2a 2a^2+2a+2 2a^2 2a+2 2a^2+2a 2a 2a^2 2a^2+2 2a^2+2  2 2a^2+2a+2 2a^2+2a 2a^2+2a+2 2a^2+2a+2
 0  0  2  0  0 2a^2+2 2a^2+2a+2 2a^2+2a 2a^2+2a  2 2a+2 2a^2+2  0  2 2a^2+2a+2 2a^2 2a 2a^2+2 2a^2 2a+2  2  2  2 2a+2 2a^2+2a 2a+2 2a 2a^2 2a^2+2  0
 0  0  0  2  0  2 2a^2+2a+2 2a 2a+2 2a^2 2a^2+2  0 2a^2+2a+2  2 2a 2a^2+2a 2a^2+2a 2a^2+2a 2a^2+2a  0 2a^2+2a+2 2a^2+2a+2 2a 2a^2+2a  0 2a^2+2a+2 2a^2 2a^2 2a^2 2a^2+2
 0  0  0  0  2 2a^2+2 2a+2 2a 2a^2+2a+2 2a 2a^2 2a^2 2a+2  0 2a  0 2a^2 2a^2+2a 2a^2+2a+2  2 2a^2 2a^2+2 2a^2+2 2a^2+2a+2 2a^2+2a  2 2a^2+2a 2a^2 2a+2  0

generates a code of length 30 over GR(64,4) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+735x^176+2142x^184+3164x^192+4410x^200+28672x^203+6209x^208+200704x^211+7434x^216+5607x^224+2590x^232+476x^240

The gray image is a code over GF(8) with n=240, k=6 and d=176.
This code was found by Heurico 1.16 in 15.9 seconds.