The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+226x^27+138x^28+358x^29+159x^30+420x^31+104x^32+332x^33+54x^34+132x^35+36x^36+62x^37+11x^38+4x^39+9x^40+2x^43

The gray image is a code over GF(2) with n=124, k=11 and d=54.
This code was found by Heurico 1.11 in 110 seconds.