The generator matrix

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

generates a code of length 49 over Z2[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+34x^37+119x^38+218x^39+318x^40+426x^41+603x^42+724x^43+760x^44+906x^45+981x^46+1152x^47+1294x^48+1220x^49+1247x^50+1234x^51+1080x^52+994x^53+856x^54+640x^55+543x^56+370x^57+256x^58+170x^59+90x^60+74x^61+32x^62+22x^63+8x^64+8x^65+2x^66+1x^68+1x^76

The gray image is a linear code over GF(2) with n=98, k=14 and d=37.
This code was found by an older version of Heurico in 0 seconds.