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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+118x^62+217x^64+8x^65+279x^66+128x^67+468x^68+200x^69+542x^70+320x^71+501x^72+280x^73+365x^74+64x^75+230x^76+24x^77+145x^78+94x^80+75x^82+21x^84+10x^86+3x^88+1x^90+1x^94+1x^116

The gray image is a linear code over GF(2) with n=284, k=12 and d=124.
This code was found by Heurico 1.16 in 21.2 seconds.