The generator matrix

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

generates a code of length 88 over F8[X]/(X^2) who´s minimum homogenous weight is 596.

Homogenous weight enumerator: w(x)=1x^0+3304x^596+2688x^597+56x^598+224x^599+812x^600+2520x^601+3248x^602+5656x^603+19376x^604+8736x^605+1456x^606+2688x^607+5684x^608+6272x^609+5600x^610+9184x^611+26488x^612+12432x^613+2296x^614+3360x^615+4823x^616+8120x^617+5936x^618+9016x^619+26208x^620+13888x^621+3360x^622+4480x^623+6986x^624+8176x^625+6720x^626+8400x^627+24976x^628+8848x^629+49x^632+35x^640+21x^648+14x^656+7x^664

The gray image is a linear code over GF(8) with n=704, k=6 and d=596.
This code was found by Heurico 1.16 in 19 seconds.