The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^25+259x^26+244x^27+302x^28+272x^29+238x^30+208x^31+136x^32+126x^33+79x^34+12x^35+8x^36+12x^37+1x^40

The gray image is a code over GF(2) with n=116, k=11 and d=50.
This code was found by Heurico 1.11 in 8.9 seconds.