The generator matrix

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

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+166x^27+211x^28+378x^29+172x^30+288x^31+245x^32+260x^33+72x^34+118x^35+52x^36+66x^37+12x^38+4x^39+2x^40+1x^44

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 51.5 seconds.