The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^28+176x^29+192x^30+176x^31+183x^32+152x^33+62x^34+6x^36+8x^37+2x^42

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.