The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+78x^57+789x^58+2254x^59+4877x^60+8686x^61+13644x^62+20228x^63+28500x^64+33358x^65+36285x^66+34324x^67+28690x^68+20954x^69+14267x^70+7750x^71+4018x^72+1984x^73+840x^74+346x^75+153x^76+58x^77+27x^78+26x^79+1x^80+2x^82+2x^85+2x^86

The gray image is a linear code over GF(2) with n=528, k=18 and d=228.
This code was found by Heurico 1.16 in 554 seconds.