The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+67x^62+148x^63+262x^64+372x^65+463x^66+432x^67+335x^68+352x^69+368x^70+264x^71+145x^72+216x^73+198x^74+160x^75+114x^76+80x^77+49x^78+20x^79+35x^80+4x^81+7x^82+3x^84+1x^88

The gray image is a linear code over GF(2) with n=276, k=12 and d=124.
This code was found by Heurico 1.16 in 0.869 seconds.