The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1 X+2  1  X  X  1  1  1  1  1  1  1  1  X  2  2  1  0  1
 0  1  1  0 X+1  1 X+3  0  1  3  1  X X+1  1  X  1  1  1  3  X X+2 X+2  1 X+2 X+3  2  1  1  X  1  1
 0  0  X  0  0  0  0  X  X X+2 X+2  2  X X+2 X+2 X+2  2  0  2  2  X  0  X  2 X+2  X  X  0  X  0  2
 0  0  0  X  0 X+2 X+2  X  X  X  2 X+2  X X+2  2  0  X  X  2 X+2 X+2  2  2  0  2  0  2  X X+2  2  X
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  0  2  2
 0  0  0  0  0  2  0  0  0  2  0  2  0  2  0  0  2  2  2  0  0  2  0  0  2  0  0  2  0  2  2
 0  0  0  0  0  0  2  0  2  0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  2  0  2  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+56x^23+144x^24+264x^25+448x^26+782x^27+1249x^28+1796x^29+2254x^30+2380x^31+2227x^32+1804x^33+1318x^34+832x^35+436x^36+220x^37+74x^38+44x^39+35x^40+12x^41+2x^42+2x^43+3x^44+1x^56

The gray image is a code over GF(2) with n=124, k=14 and d=46.
This code was found by Heurico 1.16 in 5.08 seconds.