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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+86x^44+48x^45+165x^46+146x^47+347x^48+242x^49+663x^50+420x^51+1269x^52+548x^53+2240x^54+604x^55+2761x^56+668x^57+2215x^58+576x^59+1327x^60+432x^61+676x^62+258x^63+294x^64+98x^65+133x^66+44x^67+51x^68+12x^69+36x^70+3x^72+13x^74+3x^76+3x^78+2x^80

The gray image is a linear code over GF(2) with n=224, k=14 and d=88.
This code was found by Heurico 1.16 in 16.7 seconds.