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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+54x^44+10x^45+124x^46+90x^47+209x^48+214x^49+362x^50+446x^51+689x^52+938x^53+1128x^54+1500x^55+1491x^56+1772x^57+1632x^58+1542x^59+1153x^60+942x^61+585x^62+434x^63+374x^64+206x^65+201x^66+74x^67+99x^68+14x^69+50x^70+8x^71+21x^72+10x^74+2x^75+5x^76+1x^78+3x^82

The gray image is a linear code over GF(2) with n=228, k=14 and d=88.
This code was found by Heurico 1.16 in 16.8 seconds.