The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+164x^25+317x^26+388x^27+707x^28+972x^29+773x^30+368x^31+181x^32+126x^33+61x^34+28x^35+7x^36+2x^41+1x^46

The gray image is a code over GF(2) with n=232, k=12 and d=100.
This code was found by Heurico 1.16 in 41.6 seconds.