The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+22x^22+44x^24+32x^25+41x^26+64x^27+288x^28+64x^29+285x^30+64x^31+27x^32+32x^33+22x^34+16x^36+12x^38+8x^40+1x^42+1x^46

The gray image is a code over GF(2) with n=116, k=10 and d=44.
This code was found by Heurico 1.16 in 0.0402 seconds.