The generator matrix

 1  0  1  1 2X+2  1  2  1  1  1  1  0  1  1 2X+2  1  1 2X+2 3X  1  1 3X+2  1  1 X+2 2X  1  1 3X
 0  1  1 3X+2  1 3X+3  1 2X+2 X+1  X 2X+3  1  0 X+1  1 3X+2 2X+3  1  1 X+3 2X+3  1 X+3 3X+2  1 2X+2  2 3X+1  1
 0  0  X  0 3X  X X+2 3X 2X 3X 2X  2  2 2X+2 2X+2  2 2X+2 3X 3X+2  0 3X+2 2X X+2 X+2  2  X 2X+2 3X  X
 0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0  0

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+445x^26+368x^27+956x^28+672x^29+882x^30+368x^31+316x^32+73x^34+6x^36+8x^38+1x^40

The gray image is a code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.16 in 42.4 seconds.