The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+466x^26+1978x^27+4440x^28+7648x^29+11767x^30+12656x^31+12200x^32+7936x^33+4084x^34+1694x^35+538x^36+80x^37+31x^38+4x^39+5x^40+4x^42+4x^43

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 13.5 seconds.