The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+81x^26+16x^27+118x^28+192x^29+450x^30+352x^31+450x^32+192x^33+96x^34+16x^35+66x^36+6x^38+4x^40+7x^42+1x^48

The gray image is a code over GF(2) with n=248, k=11 and d=104.
This code was found by Heurico 1.16 in 68.7 seconds.