The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  2  0  X
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  0  X X+2  2 X+2  2  X  2  2  X  0  0  2  X X+2  X  X X+2
 0  0  X  0  0  0  X X+2  X  2  X X+2  0 X+2  0  X  2 X+2  2 X+2  X  0 X+2  2 X+2  X  0  2  X  X  2
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  X X+2  X  X  X  0  2  2  X  0 X+2  X  0  X  2  2 X+2 X+2
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2  2 X+2  0  2  0  0 X+2  2 X+2  X  X  0 X+2  2  2  0 X+2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  0  2  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  2  0  0  2  0  0  0  2  0  2  2  2  2  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+48x^23+122x^24+190x^25+216x^26+352x^27+463x^28+824x^29+1238x^30+1248x^31+1287x^32+868x^33+434x^34+352x^35+215x^36+152x^37+90x^38+48x^39+22x^40+14x^41+6x^42+1x^44+1x^52

The gray image is a code over GF(2) with n=124, k=13 and d=46.
This code was found by Heurico 1.16 in 1.9 seconds.