The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  0  1  2  1 X+2  1  1  2  0  1  X X+2  1  1  1 X+2  1  X  1  1  1
 0  1  0  0  3 X+1  1  0 X+3  2  1 X+1  1 X+2  1 X+2 X+1  1  1  X  1  1  3  2 X+1  2  X  1  1  1  3
 0  0  1  1  3  2  3  1 X+3  0  3 X+2  2 X+1 X+2 X+1  X X+1 X+1  0 X+2  0  2 X+2  2  1  X X+3  1  0  X
 0  0  0  X  X  0  X X+2  2  X  2  X  X  0  0  X  2  2 X+2  2  X  0  2  0  X  0  X X+2  0 X+2  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+200x^27+139x^28+430x^29+129x^30+380x^31+123x^32+298x^33+78x^34+174x^35+39x^36+38x^37+1x^38+12x^39+2x^40+2x^41+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 1.16 in 0.418 seconds.