The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+65x^44+188x^45+435x^46+722x^47+1017x^48+1416x^49+1891x^50+2536x^51+2946x^52+3338x^53+3551x^54+3362x^55+3166x^56+2506x^57+1947x^58+1486x^59+863x^60+610x^61+360x^62+132x^63+92x^64+70x^65+34x^66+18x^67+10x^68+6x^70

The gray image is a linear code over GF(2) with n=216, k=15 and d=88.
This code was found by Heurico 1.16 in 35.6 seconds.