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

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+68x^62+236x^64+28x^65+342x^66+124x^67+453x^68+216x^69+552x^70+280x^71+488x^72+236x^73+334x^74+108x^75+246x^76+32x^77+170x^78+73x^80+60x^82+28x^84+10x^86+10x^88+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 1.49 seconds.