The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+216x^29+60x^30+32x^31+63x^32+96x^33+40x^37+4x^38

The gray image is a code over GF(2) with n=124, k=9 and d=58.
This code was found by Heurico 1.16 in 37.2 seconds.