The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+51x^22+30x^23+130x^24+136x^25+309x^26+348x^27+642x^28+884x^29+900x^30+1288x^31+939x^32+900x^33+678x^34+356x^35+280x^36+124x^37+87x^38+26x^39+50x^40+4x^41+21x^42+6x^44+2x^46

The gray image is a code over GF(2) with n=124, k=13 and d=44.
This code was found by Heurico 1.16 in 1.78 seconds.