The generator matrix

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

generates a code of length 75 over F8[X]/(X^2) who´s minimum homogenous weight is 496.

Homogenous weight enumerator: w(x)=1x^0+231x^496+168x^497+112x^500+112x^501+1400x^503+2009x^504+1624x^505+1120x^506+3360x^508+2464x^509+6832x^511+4200x^512+3696x^513+5600x^514+8064x^516+4480x^517+11424x^519+7315x^520+7056x^521+21280x^522+23520x^524+11872x^525+22736x^527+11137x^528+10472x^529+29344x^530+22288x^532+9744x^533+14952x^535+6937x^536+5656x^537+252x^544+231x^552+203x^560+126x^568+35x^576+70x^584+21x^592

The gray image is a linear code over GF(8) with n=600, k=6 and d=496.
This code was found by Heurico 1.16 in 17.9 seconds.