The generator matrix

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

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+73x^26+396x^27+331x^28+616x^29+406x^30+634x^31+311x^32+544x^33+309x^34+256x^35+91x^36+104x^37+12x^38+10x^39+2x^40

The gray image is a code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.11 in 0.123 seconds.