The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^27+334x^28+560x^29+528x^30+1000x^31+696x^32+560x^33+176x^34+92x^35+45x^36+11x^40+1x^44

The gray image is a code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 0.14 seconds.