The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+40x^44+310x^45+716x^46+1250x^47+1564x^48+2124x^49+2382x^50+2906x^51+3281x^52+3606x^53+3137x^54+3068x^55+2558x^56+2358x^57+1498x^58+870x^59+493x^60+310x^61+161x^62+72x^63+31x^64+10x^65+10x^66+8x^67+2x^69+2x^71

The gray image is a linear code over GF(2) with n=212, k=15 and d=88.
This code was found by Heurico 1.16 in 30.7 seconds.