The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  2  X  0  1  X  1  1 X+2  1  1  0  X  1  2  1  0 X+2  1  1
 0  1  0  0  2  1  3  1 X+2  X  3 X+3  1  1 X+2 X+1  1  0 X+2  1 X+1 X+3  0  2  1  2 X+3  1  1 X+1  X
 0  0  1  0  3  1  2  3  0  1 X+2 X+1  X  1  1  2 X+1  X X+3  X  X  0  1  1 X+3  1  3 X+2  0  1  X
 0  0  0  1  1  2  3  3 X+1  0 X+2  3  1  X X+1  0 X+1 X+3  X  X  2 X+2 X+2 X+3 X+2 X+3  2 X+1  1  1  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+86x^26+366x^27+334x^28+664x^29+359x^30+610x^31+358x^32+554x^33+284x^34+274x^35+100x^36+76x^37+7x^38+14x^39+7x^40+2x^41

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 0.253 seconds.