The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X 2X  1  1  1  1  1  1  X  1  0  X  1  2  1  2  1  1  1
 0  X  0 X+2  2 3X+2 2X+2  X  0 3X 2X+2 X+2 X+2  X 2X 3X+2  2  X  0 X+2 2X+2  0  X 3X  X  2 X+2  X  2 2X 3X
 0  0 2X+2  0  2  2 2X  2  0 2X  0  0 2X 2X+2 2X+2 2X+2 2X+2  2  0  2  2 2X+2  0 2X 2X  2 2X 2X+2 2X 2X 2X
 0  0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0 2X  0  0  0
 0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X  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+66x^27+148x^28+280x^29+378x^30+378x^31+366x^32+216x^33+100x^34+62x^35+24x^36+16x^37+2x^38+6x^39+4x^40+1x^48

The gray image is a code over GF(2) with n=248, k=11 and d=108.
This code was found by Heurico 1.16 in 0.062 seconds.