The generator matrix

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

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+121x^44+58x^46+455x^48+56x^49+488x^50+168x^51+1198x^52+448x^53+1550x^54+896x^55+2358x^56+1008x^57+2016x^58+784x^59+1954x^60+512x^61+854x^62+192x^63+769x^64+24x^65+152x^66+8x^67+230x^68+2x^70+62x^72+17x^76+3x^80

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 18.7 seconds.