The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+226x^26+786x^27+715x^28+948x^29+482x^30+554x^31+212x^32+104x^33+59x^34+8x^35+1x^38

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 0.062 seconds.