The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+560x^76+1098x^78+1480x^80+1290x^82+1176x^84+944x^86+757x^88+460x^90+280x^92+110x^94+33x^96+2x^98+1x^104

The gray image is a linear code over GF(2) with n=332, k=13 and d=152.
This code was found by Heurico 1.16 in 41.5 seconds.