The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+606x^26+1437x^28+2068x^30+2088x^32+1430x^34+465x^36+80x^38+7x^40+8x^42+2x^44

The gray image is a code over GF(2) with n=124, k=13 and d=52.
This code was found by Heurico 1.13 in 32.8 seconds.