The generator matrix

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

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+108x^26+454x^27+1184x^28+2122x^29+2747x^30+3328x^31+2661x^32+2114x^33+1019x^34+388x^35+184x^36+34x^37+29x^38+4x^39+2x^40+2x^41+1x^42+2x^43

The gray image is a code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 1.05 seconds.