The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+283x^28+128x^29+464x^30+256x^31+551x^32+128x^33+208x^34+27x^36+1x^44+1x^52

The gray image is a code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 1.17 seconds.