The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+50x^24+58x^25+149x^26+234x^27+310x^28+418x^29+484x^30+608x^31+659x^32+716x^33+715x^34+712x^35+790x^36+676x^37+447x^38+428x^39+320x^40+170x^41+109x^42+62x^43+44x^44+10x^45+12x^46+4x^47+2x^48+3x^50+1x^54

The gray image is a linear code over GF(2) with n=68, k=13 and d=24.
This code was found by an older version of Heurico in 0 seconds.