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

generates a code of length 31 over Z4[X]/(X^2+2X+2) 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 0.031 seconds.