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

generates a code of length 53 over F8[X]/(X^2) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+63x^360+252x^368+3584x^371+175x^376+7x^400+14x^424

The gray image is a linear code over GF(8) with n=424, k=4 and d=360.
This code was found by Heurico 1.16 in 0.025 seconds.