The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 X X X^2 1 X X X X^2 X^2 X^3 0 1 1
0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0
generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 29.
Homogenous weight enumerator: w(x)=1x^0+16x^29+9x^30+4x^31+1x^34+1x^36
The gray image is a linear code over GF(2) with n=232, k=5 and d=116.
As d=119 is an upper bound for linear (232,5,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 5.
This code was found by Heurico 1.16 in 3.81e-009 seconds.