The generator matrix

 1  0  0  1  1  1  0  X  1 3X  X  1  1  1  1  1 2X+2  2 X+2 3X+2  1  1  2  1  1  1  2  1  1  1  1
 0  1  0  X  1 3X+3  1 3X+2 3X  1  1 X+3  3 2X+2  0  X  1 3X  1  1 2X 2X  1 2X 3X+1 X+1  1 2X+2  1  2  0
 0  0  1  1 2X+3  X 3X+3  1 3X+3 2X+2 3X+3 X+3  0 3X+2  3 3X+2 3X+2  1  1 X+3 X+1 X+1  2  2 3X+1  0 3X+3 2X 2X+2  X  0
 0  0  0 2X+2  2 2X 2X+2  2  2 2X+2 2X  0 2X+2 2X+2 2X 2X  2 2X 2X  2 2X  2 2X 2X+2  2 2X  0 2X 2X 2X+2  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+116x^26+478x^27+1160x^28+2042x^29+2787x^30+3424x^31+2597x^32+2066x^33+1091x^34+396x^35+144x^36+34x^37+37x^38+4x^39+2x^40+2x^41+1x^42+2x^43

The gray image is a code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 1.11 seconds.