The generator matrix

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

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+186x^28+968x^29+546x^30+1032x^31+331x^32+680x^33+148x^34+120x^35+58x^36+16x^37+10x^38

The gray image is a code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.16 in 0.078 seconds.