The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1 2X X+2  0  X  1  1 3X+2  1 3X  2  X  1  1  1  1 X+2 2X+2 3X  1
 0  1  0  0 2X  1 2X+1  1  X X+2 2X+3 X+3  1  1  X  1  3 3X+2  1 3X 2X+2  1  2 2X+2 2X+3 2X+3  0  1  1  1  0
 0  0  1  0 2X+1  1 2X  3 2X+2 3X+1  0  1 2X+2 2X+3  1 X+2 3X 2X+1  2 3X+1  X X+3  1 3X+3 3X+3 X+2 3X+2 3X+1 2X+3  3 3X+2
 0  0  0  1  1 2X 2X+1 2X+1  3 3X 3X+2 3X+3 X+1  X X+1 X+3 2X+1 3X+1 2X  2  1  X 3X+1 3X+3  0 X+3  2 X+1 3X+3 2X+1 3X+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+506x^26+2046x^27+4080x^28+8030x^29+11317x^30+13348x^31+11656x^32+8288x^33+3918x^34+1654x^35+482x^36+158x^37+33x^38+8x^39+5x^40+4x^41+2x^42

The gray image is a code over GF(2) with n=248, k=16 and d=104.
This code was found by Heurico 1.16 in 15.4 seconds.