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

generates a code of length 51 over F8[X]/(X^2) who´s minimum homogenous weight is 340.

Homogenous weight enumerator: w(x)=1x^0+3024x^340+5152x^341+56x^343+658x^344+1344x^345+6608x^346+6496x^347+16240x^348+18368x^349+448x^350+784x^351+3171x^352+4480x^353+13664x^354+8512x^355+24304x^356+30240x^357+3136x^358+2744x^359+7280x^360+8512x^361+22736x^362+13664x^363+31696x^364+28672x^365+84x^368+28x^376+21x^384+7x^392+7x^400+7x^408

The gray image is a linear code over GF(8) with n=408, k=6 and d=340.
This code was found by Heurico 1.16 in 9.57 seconds.