The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+196x^71+432x^72+726x^73+1206x^74+1260x^75+1748x^76+1994x^77+2536x^78+2326x^79+3031x^80+2392x^81+2624x^82+2442x^83+2576x^84+1858x^85+1659x^86+1292x^87+948x^88+566x^89+403x^90+208x^91+180x^92+74x^93+45x^94+18x^95+8x^96+4x^97+7x^98+2x^99+4x^100+2x^101

The gray image is a linear code over GF(2) with n=324, k=15 and d=142.
This code was found by Heurico 1.16 in 54.3 seconds.