The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+127x^24+854x^25+2838x^26+7220x^27+16690x^28+29720x^29+47659x^30+51526x^31+47696x^32+30512x^33+16832x^34+6872x^35+2544x^36+680x^37+251x^38+94x^39+14x^40+10x^41+4x^42

The gray image is a code over GF(2) with n=248, k=18 and d=96.
This code was found by Heurico 1.16 in 217 seconds.