The generator matrix

 1  0  0  1  1  1  2  0  1  1  2  1  1  0  X X+2  1  0  1  1  X  2 X+2  1  0  1 X+2  X  1  1  1
 0  1  0  0  3  3  1 X+2  2  1  1  2  1  1  X  2  2  1 X+1  3 X+2  1  1  2 X+2  1  1  2 X+1 X+2  X
 0  0  1 X+1 X+3  2 X+3  1  X  3  1  1 X+2  X  1  1 X+3  2  0  1  1 X+3 X+2  2  1  0 X+2  1 X+2  2  2
 0  0  0  2  2  0  2  2  2  0  0  0  2  2  0  2  0  2  2  2  2  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 28.

Homogenous weight enumerator: w(x)=1x^0+243x^28+336x^30+240x^32+120x^34+61x^36+8x^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 1.16 in 0.254 seconds.