The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  1  1  2 3X+2  1  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 3X+2 X+1 2X+1  1  1 3X 3X 3X  0 3X+2  0  0
 0  0 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0
 0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0  0  0 2X  0
 0  0  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X  0  0  0
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0  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+51x^26+88x^27+160x^28+704x^29+564x^30+976x^31+557x^32+704x^33+148x^34+88x^35+46x^36+2x^38+2x^40+1x^42+2x^44+2x^46

The gray image is a code over GF(2) with n=248, k=12 and d=104.
This code was found by Heurico 1.16 in 0.093 seconds.