The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+62x^27+117x^28+138x^29+162x^30+162x^31+183x^32+160x^33+134x^34+146x^35+168x^36+168x^37+126x^38+126x^39+94x^40+40x^41+26x^42+16x^43+11x^44+6x^45+2x^48

The gray image is a linear code over GF(2) with n=68, k=11 and d=27.
This code was found by an older version of Heurico in 0 seconds.