The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+316x^76+456x^78+434x^80+300x^82+188x^84+136x^86+100x^88+60x^90+44x^92+8x^94+1x^96+4x^100

The gray image is a linear code over GF(2) with n=324, k=11 and d=152.
This code was found by Heurico 1.11 in 0.312 seconds.