The generator matrix

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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+142x^53+500x^54+670x^55+905x^56+1152x^57+1231x^58+1382x^59+1485x^60+1612x^61+1555x^62+1394x^63+1168x^64+1042x^65+847x^66+516x^67+341x^68+202x^69+107x^70+60x^71+34x^72+10x^73+14x^74+10x^75+2x^76+2x^78

The gray image is a linear code over GF(2) with n=244, k=14 and d=106.
This code was found by Heurico 1.13 in 3.56 seconds.