The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+21x^22+8x^23+31x^24+32x^25+21x^26+816x^27+19x^28+32x^29+12x^30+8x^31+4x^32+7x^34+9x^36+2x^38+1x^46

The gray image is a code over GF(2) with n=216, k=10 and d=88.
This code was found by Heurico 1.16 in 0.438 seconds.