The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  X  X  1  X  1
 0  X  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  X  X  X X^2+X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2+X  X  X  0  0  0  X  X X^2+X X^2  0  X  0 X^2+X  0  0
 0  0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2+X  X  0 X^2 X^2  0 X^2+X X^2+X X^2+X  X X^2  0  X X^2  0  X X^2+X X^2  0 X^2  X X^2  X  X X^2+X X^2+X X^2  X  0  X X^2+X  X  0  0
 0  0  0  X  0  0  0  X X^2+X  X  X  X  0  X X^2  X  0  0 X^2+X X^2 X^2 X^2 X^2+X  X  X  X X^2 X^2+X X^2  X  0  0  0 X^2 X^2  0  0 X^2  0  X  0  0  X X^2+X  0  X X^2+X  0  0
 0  0  0  0  X  0  X  X  X X^2  X X^2  X X^2+X X^2 X^2 X^2+X  X X^2+X  X X^2 X^2 X^2  0 X^2+X X^2+X  0  X X^2+X  X  0  0  X X^2  X X^2 X^2 X^2 X^2+X X^2  X X^2+X X^2  X X^2+X X^2 X^2  X  0
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  0  X  0  X X^2+X  0 X^2+X X^2+X  0  0 X^2 X^2  X  0  0  0 X^2  0  X X^2 X^2+X  X  X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  X X^2+X  X  X X^2+X X^2 X^2+X  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0

generates a code of length 49 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+53x^38+76x^39+205x^40+262x^41+354x^42+360x^43+412x^44+592x^45+944x^46+1592x^47+2129x^48+2396x^49+2096x^50+1628x^51+992x^52+624x^53+436x^54+360x^55+303x^56+206x^57+198x^58+76x^59+52x^60+16x^61+14x^62+4x^63+2x^64+1x^86

The gray image is a linear code over GF(2) with n=196, k=14 and d=76.
This code was found by Heurico 1.16 in 13.8 seconds.