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  X  1  1  1  1  1  1  1  1  1
 0  1  1  a a^6*X+a^2 a^3 a^6*X+a^4 a^5 a^6*X+a^6  a a^6*X+a^2  0 a^6*X+1 a^5 a^6*X+a^4 a^6*X+a^6 a^3  1 a^6*X+1 a^5 a^3  a a^6*X+a^2 a^6*X+a^6 a^6*X+a^4 X+a^5 X+a X+a^3 a^5*X+a^6 a^6*X+1  1 a^5*X+a^4 a*X+a^5 a^5*X+a^2  0  1 a^5*X+a^2 a^4*X+a^6 a^5*X+1  X a^3*X+1 a^6*X+a^2 X+a^2 a^4*X+a^2  0
 0  0 a^6*X  0  X  X a^3*X  X a^2*X a^3*X a^6*X a^2*X a^2*X  0  0 a^2*X a^6*X  X  X a*X a^3*X a^4*X a^3*X a*X a^5*X  0 a^6*X a^3*X a^4*X a^4*X a^2*X  0  X  0 a^4*X a^6*X a^2*X a^3*X a^4*X a^2*X a^3*X  X a^5*X a^6*X  0
 0  0  0  X a^6*X a^5*X a^3*X a^2*X a^5*X a^6*X a^6*X a^4*X a*X a^2*X a^5*X  0 a^4*X a^5*X a*X a^3*X  0 a^4*X  X a^6*X a^5*X a*X a^3*X a^2*X a^6*X a^3*X  0 a^3*X a^4*X a^2*X a*X a^5*X  X a^5*X  0 a*X a^3*X a^5*X  X a*X a^2*X

generates a code of length 45 over F8[X]/(X^2) 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 linear code over GF(8) with n=360, k=6 and d=288.
This code was found by Heurico 1.16 in 10.4 seconds.