The generator matrix

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

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+24x^29+270x^30+48x^31+77x^32+24x^33+66x^34+2x^44

The gray image is a code over GF(2) with n=248, k=9 and d=116.
This code was found by Heurico 1.16 in -3.24e-008 seconds.