The generator matrix

 1  0  0  1  1  1  X  X  1  1  1  2  2 X+2  0  1  1 X+2  2  2  1  1  X  1  2  1  1  1  2  1 X+2
 0  1  0  0  1  1  1  1 X+1  X X+3  1  X  1  1  X X+3  2  1  2  X  0  1  2  1 X+2  X  3  1 X+1  1
 0  0  1 X+1 X+3  0  1  X X+3  1  X  1  1 X+1 X+2  X  3  1  3  1 X+3  3  0 X+2  X  2  1  0 X+3  0 X+1
 0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  2  2  2  0  0  2
 0  0  0  0  2  0  0  0  2  0  0  0  2  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  0  0  0  0  2  0  0  0  2  2  0  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+158x^26+268x^27+386x^28+500x^29+516x^30+536x^31+485x^32+488x^33+320x^34+220x^35+134x^36+36x^37+28x^38+18x^40+2x^42

The gray image is a code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.16 in 0.295 seconds.