The generator matrix

 1  0  0  1  1  1  0 X^3  0 X^2  1  1  1  1 X^3+X  1 X^3+X  1  1  1 X^3+X^2+X X^2+X X^3+X^2+X  X  1  1  1  1  1  1  1  1  0  1  X  1 X^3+X^2 X^3  1 X^3+X^2  1 X^3+X^2+X  1 X^3+X^2+X  1 X^2 X^3  1  1  1 X^3+X^2+X  1  X  1  1  1  1 X^3+X^2+X X^3+X  1 X^3+X  1  1  1 X^3+X^2  1 X^3+X^2+X  X  1
 0  1  0  0 X^2+1 X^3+X^2+1  1 X^2+X  1  1 X^3  0 X^3+1 X^3+1 X^3+X^2+X  X  1  X X+1 X^2+X+1  1 X^2  1  1 X^3+X^2+X+1 X^3+X^2+X+1 X^2+X X^2 X^3+X  0  1 X^3+1 X^3+X^2  1  1 X^3  1  1 X^2+X X^3+X X^3+X X^2  1  1 X+1  1  1 X^3+X^2+X+1 X^3+X+1 X^3+X^2+X  1 X^3+X^2+X  1 X^2  0  1 X^3  1  1  1  1 X^3+X^2+X+1 X^3+X^2+X X^3  1 X^3+X^2 X^3 X^2+X  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^3+X^2+X  1 X^2+X X^2+1  X X^2+1  1 X^2+X+1 X^3+X X^3+X X^3 X^3+X+1 X^3+X^2+1  1 X^3 X^3+X+1  X X^3+X^2+1 X^3+1 X^3 X^3+X^2  1 X^3 X^3+X^2+1  1 X^3+X^2+X X+1 X^2+X X^3+X+1 X^3 X^3+X+1  1 X+1  1 X^3+X^2+X+1 X^3+1 X+1 X^3+X^2+1 X^3+X  1 X^3+1 X^3+X X^3+X^2+1 X^3+X^2+1 X^2 X^3+X X^3+X+1 X^2+1 X^3 X^3+X+1 X^3+X^2+X X^2+X+1 X^3 X^3+X^2  X X+1 X^3+X^2+X+1 X^3+X^2+1  1  1  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3 X^3  0  0 X^3 X^3 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3+X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^2 X^3+X^2  0 X^2  0 X^3+X^2  0 X^2 X^3 X^2  0

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+80x^63+736x^64+1016x^65+1764x^66+1768x^67+2115x^68+1976x^69+2172x^70+1532x^71+1325x^72+732x^73+594x^74+252x^75+161x^76+60x^77+68x^78+10x^80+8x^81+10x^82+4x^84

The gray image is a linear code over GF(2) with n=552, k=14 and d=252.
This code was found by Heurico 1.16 in 6.69 seconds.