The generator matrix

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

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+149x^28+386x^30+362x^32+76x^34+47x^36+2x^38+1x^56

The gray image is a code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.016 seconds.