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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+47x^52+68x^53+126x^54+160x^55+194x^56+304x^57+310x^58+318x^59+365x^60+398x^61+395x^62+330x^63+294x^64+250x^65+123x^66+118x^67+92x^68+50x^69+53x^70+30x^71+27x^72+14x^73+10x^74+4x^75+4x^76+4x^77+6x^78+1x^90

The gray image is a linear code over GF(2) with n=244, k=12 and d=104.
This code was found by Heurico 1.16 in 1.17 seconds.