The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  0  X  0  1  X  0
 0  X  0 3X+2 2X X+2  0  X  2 3X+2 2X+2 3X 2X+2 2X+2 3X+2 3X+2 3X 3X+2  X 2X X+2  X X+2 3X+2 3X+2  X  2  X 2X+2  X  X
 0  0 2X+2  0  0 2X+2  2  2  2  2 2X  0 2X+2 2X  2 2X 2X+2 2X+2  0 2X  0 2X 2X+2  2 2X+2 2X+2  2  2  2 2X+2  0
 0  0  0 2X+2  2  2  2 2X  0  0 2X 2X+2  2 2X+2 2X+2  0  2 2X  2  0 2X 2X+2  2 2X  0 2X+2 2X+2  2 2X+2  0 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+351x^28+64x^29+400x^30+384x^31+531x^32+64x^33+176x^34+69x^36+7x^40+1x^48

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 98.3 seconds.