The generator matrix

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

generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+72x^59+727x^60+2362x^61+5121x^62+7996x^63+14183x^64+19804x^65+28855x^66+33446x^67+37010x^68+33302x^69+28640x^70+20534x^71+14726x^72+7856x^73+4332x^74+1710x^75+893x^76+338x^77+151x^78+46x^79+10x^80+12x^81+5x^82+4x^83+2x^84+6x^85

The gray image is a linear code over GF(2) with n=544, k=18 and d=236.
This code was found by Heurico 1.16 in 589 seconds.