The generator matrix

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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+42x^61+610x^62+1016x^63+1793x^64+1768x^65+2347x^66+1920x^67+2307x^68+1400x^69+1413x^70+648x^71+534x^72+280x^73+160x^74+80x^75+41x^76+14x^77+5x^78+2x^80+2x^84+1x^90

The gray image is a linear code over GF(2) with n=536, k=14 and d=244.
This code was found by Heurico 1.16 in 12.5 seconds.