The generator matrix

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

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+160x^26+220x^27+464x^28+460x^29+590x^30+436x^31+515x^32+480x^33+352x^34+172x^35+176x^36+20x^37+30x^38+4x^39+12x^40+4x^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 0.285 seconds.