The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  X  1  X X^2  1  0  X X^2 X^3  1 X^2  X  X X^2  1
 0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2 X^2  0 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^2 X^2 X^2 X^3  0 X^3  0  0

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+2x^30+44x^31+3x^32+12x^33+2x^34

The gray image is a linear code over GF(2) with n=248, k=6 and d=120.
This code was found by Heurico 1.16 in 6.87e-008 seconds.