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

generates a code of length 57 over F8[X]/(X^2) who´s minimum homogenous weight is 352.

Homogenous weight enumerator: w(x)=1x^0+175x^352+1085x^360+2212x^368+2961x^376+448x^378+3542x^384+9408x^386+4011x^392+65856x^394+4592x^400+153664x^402+5061x^408+4088x^416+2835x^424+1610x^432+504x^440+84x^448+7x^456

The gray image is a linear code over GF(8) with n=456, k=6 and d=352.
This code was found by Heurico 1.16 in 35 seconds.