The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2  X  1  0  1  1  1  1  X  X  1 X^2+2
 0  X  0  X  0 X^2 X^2+X X^2+X X^2 X^2+2  0 X+2  2  X X^2+X+2 X^2+X+2 X^2+2  2 X^2+X  X X^2+X+2  0  X X^2+2 X^2+2 X^2+2 X^2 X+2 X^2+X+2  X  2
 0  0  X  X X^2+2  X X^2+X  0 X^2 X^2+X  2 X^2+X X^2+X+2 X^2+X X^2 X^2 X+2  X X^2+X+2 X^2+2 X^2 X+2 X^2+X  0 X^2+X X^2+X X^2+X+2  2  X X^2+2  X
 0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  2  2  0  2  2  0  2  0  2  0  0  2  0  2  2  0
 0  0  0  0  2  2  2  2  0  2  2  2  0  0  2  0  2  0  0  2  0  2  2  0  2  0  0  2  2  2  2

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+208x^27+247x^28+628x^29+540x^30+958x^31+559x^32+546x^33+112x^34+172x^35+68x^36+40x^37+4x^38+6x^39+4x^40+2x^41+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 35.6 seconds.