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 2X 0 0 0 0 0 0 0 0 2X 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 2X 2X 2X 0 0 0
0 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 0 2X 2X 0
0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 0
0 0 0 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 0 2X 0 0 2X 2X 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 0 0 0 2X 2X
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X
0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 2X 0 0 0 2X 0 2X 2X 2X
generates a code of length 29 over Z4[X]/(X^2+2) 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+1088x^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=232, k=11 and d=88.
This code was found by Heurico 1.16 in 0.062 seconds.