The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+249x^28+224x^29+432x^30+320x^31+368x^32+224x^33+168x^34+51x^36+8x^38+3x^40

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 0.031 seconds.