The generator matrix

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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+16x^62+8x^63+3x^64+4x^66

The gray image is a linear code over GF(2) with n=244, k=5 and d=124.
As d=125 is an upper bound for linear (244,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.0879 seconds.