The generator matrix

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

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+57x^26+32x^27+207x^28+128x^29+403x^30+448x^31+401x^32+128x^33+125x^34+32x^35+48x^36+17x^38+14x^40+6x^42+1x^44

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 0.063 seconds.