The generator matrix
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 X X^2 X^2 X^2 1 X X X X 1 1 X X X X X X^2 X X X
0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 0
0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0
generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.
Homogenous weight enumerator: w(x)=1x^0+6x^46+44x^47+7x^48+4x^51+2x^62
The gray image is a linear code over GF(2) with n=376, k=6 and d=184.
This code was found by Heurico 1.16 in 0.031 seconds.