The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+123x^74+228x^75+527x^76+448x^77+709x^78+620x^79+714x^80+604x^81+761x^82+516x^83+638x^84+488x^85+467x^86+360x^87+305x^88+220x^89+188x^90+64x^91+102x^92+32x^93+44x^94+4x^95+12x^96+8x^98+5x^100+4x^102

The gray image is a linear code over GF(2) with n=328, k=13 and d=148.
This code was found by Heurico 1.16 in 4.24 seconds.