The generator matrix

 1  0  1  1  1 2X 3X+2  1  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X+2 2X+3  1  1 2X  3 3X+2  1 2X+1 3X+3 X+1 X+3  1 2X+2 3X 3X  0  0 3X+2  2  X  3  2  2  3  1 3X+1  0
 0  0 2X+2  2 2X 2X+2  0 2X+2  2  0  2 2X  2  0 2X 2X+2 2X+2 2X  0  2 2X 2X+2  0  2 2X+2  2 2X  0  2  2  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+53x^28+164x^29+187x^30+218x^31+184x^32+160x^33+51x^34+2x^35+2x^36+1x^38+1x^54

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.