The generator matrix

0 X 1 1 1 1 0 0 0 1 0 1 0 1 1 X 0 1 1 1 1 0 X X 1 0 X 1 1 0 1 0 0 X 1 1 0 X 1 X X 1 X 0 1 0 0 1 0 0 0 0 1 1 0 1 X 0 X 1 1 0 0 X X 1
1 0 0 1 X 1 1 X X X+1 X 1 1 X 0 1 1 X X 1 X+1 X X 1 X 0 0 1 X+1 1 X+1 1 X X X X X X X+1 1 X X+1 0 0 X 1 1 X 1 0 1 1 X+1 X+1 X 1 1 X 1 0 1 1 X X 1 0
X X X 0 1 1 X+1 1 0 0 1 1 1 1 X X X 0 1 X+1 1 1 X 1 X X 1 0 X 0 1 1 X 1 1 X 1 1 X X+1 1 X X X 0 0 X 0 0 X X+1 X X X+1 0 1 X 1 1 X X 1 1 1 X+1 0
0 1 1 0 0 X+1 1 0 1 X 0 1 X+1 0 X+1 0 0 X+1 X X+1 1 0 1 1 X+1 1 X 0 0 X X+1 1 0 0 X+1 X 1 1 1 X X+1 1 0 0 0 X+1 X+1 X 0 1 X+1 1 1 X+1 1 X 1 X X+1 X+1 X+1 X 1 0 0 0
0 0 0 0 0 0 X X X+1 X+1 X+1 X+1 X+1 X+1 1 X+1 0 X+1 1 X 1 X+1 X X X 1 0 X+1 X X+1 X+1 X+1 1 0 1 X X+1 X+1 X+1 X+1 X 0 X 1 1 0 X+1 X+1 X X+1 X+1 1 X X+1 X+1 1 X X+1 X+1 1 1 X 1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 X 0 0 X X 1 X+1 1 1 X+1 1 1 1 1 X+1 X+1 1 1 X+1 X 1 X+1 X 0 X+1 1 X 0 X X+1 X+1 1 0 0 X+1 X+1 1 X 1 X 0 X+1 X+1 1 1 0 X 1 1 X+1 X+1 0 X+1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 X X 0 X X 0 0 X 0 0 0 X 0 0 0 X+1 1 X+1 X+1 X+1 1 X+1 X+1 1 X+1 X+1 1 X+1 X+1 1 X+1 1 X+1 1 1 X X+1 X+1 1 1 X+1 X 1 X X+1 X+1 1 0 0

generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+50x^53+125x^54+280x^55+347x^56+406x^57+553x^58+590x^59+712x^60+810x^61+851x^62+918x^63+988x^64+936x^65+1041x^66+1116x^67+1032x^68+1024x^69+882x^70+790x^71+682x^72+602x^73+493x^74+372x^75+285x^76+186x^77+130x^78+92x^79+42x^80+16x^81+20x^82+2x^83+7x^84+2x^85+1x^106

The gray image is a linear code over GF(2) with n=132, k=14 and d=53.
This code was found by an older version of Heurico in 0 seconds.