The generator matrix

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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+112x^56+20x^58+357x^60+264x^62+882x^64+1246x^66+2458x^68+2814x^70+3088x^72+2128x^74+1573x^76+596x^78+484x^80+94x^82+165x^84+6x^86+68x^88+22x^92+5x^96+1x^100

The gray image is a linear code over GF(2) with n=284, k=14 and d=112.
This code was found by Heurico 1.16 in 25.6 seconds.