The generator matrix

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

generates a code of length 45 over GR(64,4) who´s minimum homogenous weight is 288.

Homogenous weight enumerator: w(x)=1x^0+273x^288+168x^291+896x^295+2170x^296+1064x^297+2240x^299+8064x^303+9450x^304+3528x^305+4816x^307+38528x^311+32389x^312+11256x^313+11648x^315+67200x^319+44527x^320+12824x^321+9800x^323+539x^328+378x^336+259x^344+91x^352+35x^360

The gray image is a code over GF(8) with n=360, k=6 and d=288.
This code was found by Heurico 1.16 in 10.2 seconds.