The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+176x^26+1032x^27+2377x^28+3588x^29+5776x^30+6544x^31+6282x^32+3848x^33+1986x^34+776x^35+263x^36+84x^37+28x^38+5x^40+2x^42

The gray image is a code over GF(2) with n=248, k=15 and d=104.
This code was found by Heurico 1.16 in 4.25 seconds.