The generator matrix

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

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+144x^26+1024x^27+2449x^28+3644x^29+5696x^30+6480x^31+6346x^32+3848x^33+1970x^34+784x^35+255x^36+92x^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 4.28 seconds.