The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  X  1 X^2  1  1  0  1  X  1 X^2  X  1  1 X^2+X  0  1  1  X  1  1 X^2+X  1  0  1 X^2+X  1  0  0  1  1 X^2+X  1  1  1 X^2  1 X^2  0  0  1  X  1  1  1  X  1  1 X^2 X^2+X  1  1  X X^2+X X^2+X  1  0  X  1  1  1  1  X X^2  1  1  X  1 X^2  1  1  1  1  1
 0  1  0  0  1 X^2+X+1  1 X^2  0 X^2 X^2+X+1  1  1  1 X^2 X^2  1  1  1 X^2+1 X^2+X  1 X+1 X^2+X  1 X^2 X^2+X X^2+X+1  X X^2+X+1  1  1 X^2+X  1  X  0  0  1  1 X+1 X^2+X  1  X  1 X^2+X  1 X^2+X+1  0  1  X  1  1  1 X^2+X+1  X  1  0  0  1 X^2 X^2+X+1  0  1  1 X^2 X^2  1  1 X^2+X+1 X^2+1 X^2+X  1  1  1 X^2+X+1 X^2+X+1  0 X^2+1  0  1  X X^2+X  X X^2+X
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  0  1  0  1 X^2 X+1  1  X  1 X^2  0 X^2+X X+1  1 X^2+1 X^2+1  1 X^2+X X^2+1 X^2 X^2+1 X+1  0  1 X^2+X X^2+X+1 X^2+X X+1  1  X X+1 X^2+X X^2  1 X^2+X+1  1  0  1  X  X X+1 X^2+1 X^2+1  1 X^2+X  X X^2+X+1  1 X^2 X^2+X+1 X^2+X+1 X^2  1 X^2+1  0  X  1  0  X  X X^2+X X^2+1 X^2+X X+1  1 X^2+X+1  1  1  1 X+1  X  X
 0  0  0  X  X X^2+X X^2 X^2+X  0  0  X X^2 X^2+X  0  X X^2  X  0  X X^2  X X^2+X X^2 X^2+X  X X^2+X X^2  X  X X^2  0 X^2  0 X^2+X X^2 X^2 X^2+X  X  X X^2  X  0 X^2+X  X X^2+X X^2  X X^2 X^2+X  X X^2+X  X  0 X^2+X  0 X^2  0  X  0  X  0 X^2  X X^2+X  0 X^2+X  0  0 X^2  0  0  0  X X^2 X^2 X^2 X^2+X X^2  X X^2+X X^2+X  X X^2  X
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+176x^76+168x^77+558x^78+468x^79+772x^80+436x^81+848x^82+564x^83+747x^84+464x^85+670x^86+400x^87+567x^88+284x^89+430x^90+196x^91+199x^92+48x^93+58x^94+36x^95+52x^96+8x^97+22x^98+14x^100+6x^102

The gray image is a linear code over GF(2) with n=336, k=13 and d=152.
This code was found by Heurico 1.16 in 4.39 seconds.