The generator matrix

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

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+118x^22+328x^23+1331x^24+1916x^25+4440x^26+5996x^27+10578x^28+13876x^29+18148x^30+17384x^31+18328x^32+13488x^33+11144x^34+6364x^35+4286x^36+1700x^37+1062x^38+328x^39+155x^40+60x^41+32x^42+8x^44+1x^48

The gray image is a code over GF(2) with n=124, k=17 and d=44.
This code was found by Heurico 1.13 in 76.2 seconds.