The generator matrix

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

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+124x^62+116x^63+386x^64+232x^65+422x^66+236x^67+439x^68+368x^69+398x^70+236x^71+332x^72+232x^73+274x^74+116x^75+82x^76+36x^78+21x^80+20x^82+14x^84+6x^86+3x^88+1x^92+1x^96

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 1.02 seconds.