The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+72x^23+416x^24+1048x^25+2209x^26+3278x^27+5255x^28+6838x^29+8864x^30+9036x^31+9206x^32+7280x^33+5408x^34+3210x^35+2023x^36+822x^37+332x^38+144x^39+57x^40+12x^41+19x^42+4x^43+2x^44

The gray image is a code over GF(2) with n=124, k=16 and d=46.
This code was found by Heurico 1.13 in 21.7 seconds.