The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+45x^20+2x^21+56x^22+6x^23+192x^24+62x^25+216x^26+172x^27+441x^28+506x^29+649x^30+922x^31+1125x^32+1478x^33+1340x^34+1896x^35+1367x^36+1478x^37+1173x^38+922x^39+680x^40+506x^41+440x^42+172x^43+187x^44+62x^45+163x^46+6x^47+50x^48+2x^49+52x^50+8x^52+7x^54

The gray image is a linear code over GF(2) with n=70, k=14 and d=20.
This code was found by Heurico 1.16 in 11 seconds.