The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+54x^28+132x^29+78x^30+32x^31+67x^32+72x^33+44x^34+6x^36+20x^37+6x^38

The gray image is a code over GF(2) with n=124, k=9 and d=56.
This code was found by Heurico 1.13 in 4.2e-008 seconds.