The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  X  1  X  1  X  X  X 2X+2  X  X
 0 2X  0  0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X
 0  0 2X  0  0  0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0  0 2X 2X
 0  0  0 2X  0  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X
 0  0  0  0 2X  0  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X 2X
 0  0  0  0  0 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X
 0  0  0  0  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0 2X  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+35x^26+58x^28+173x^30+512x^31+173x^32+34x^34+18x^36+10x^38+2x^40+3x^42+4x^44+1x^46

The gray image is a code over GF(2) with n=248, k=10 and d=104.
This code was found by Heurico 1.16 in 1.95 seconds.