The generator matrix

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

generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+47x^54+108x^55+196x^56+190x^57+381x^58+476x^59+597x^60+662x^61+870x^62+1162x^63+1288x^64+1430x^65+1470x^66+1640x^67+1269x^68+1092x^69+936x^70+736x^71+555x^72+370x^73+297x^74+204x^75+159x^76+86x^77+82x^78+26x^79+23x^80+10x^81+9x^82+7x^84+1x^86+1x^88+2x^90+1x^98

The gray image is a linear code over GF(2) with n=264, k=14 and d=108.
This code was found by Heurico 1.16 in 21 seconds.