The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  1  1  2  X  X  1  2  1  1  X  1  1  1  0 X+2  1  0  1  X  X
 0  1  0  0  1  1  1  X  2  3  1  2  3  1  0 X+2  1  1  X  2  2  1 X+3 X+2  1 X+2  0 X+2 X+3  1  1
 0  0  1  1  2  3  1  1  X X+2  X X+1 X+3 X+3  1  1  X  1 X+2  3  1 X+1  0  0  2  1 X+2  1  2  0  0
 0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  0  2  0  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+239x^28+340x^30+248x^32+112x^34+57x^36+12x^38+15x^40

The gray image is a code over GF(2) with n=124, k=10 and d=56.
This code was found by Heurico 1.11 in 0.183 seconds.