The generator matrix

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

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+184x^28+1068x^29+404x^30+1036x^31+301x^32+760x^33+154x^34+124x^35+42x^36+20x^37+2x^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 0.079 seconds.