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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+54x^58+28x^59+152x^60+178x^61+239x^62+334x^63+447x^64+542x^65+727x^66+960x^67+1116x^68+1318x^69+1381x^70+1458x^71+1362x^72+1326x^73+1209x^74+980x^75+706x^76+598x^77+331x^78+282x^79+220x^80+114x^81+115x^82+48x^83+64x^84+18x^85+31x^86+6x^87+18x^88+2x^89+5x^90+10x^92+2x^94+2x^98

The gray image is a linear code over GF(2) with n=284, k=14 and d=116.
This code was found by Heurico 1.16 in 24.6 seconds.