The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+198x^24+192x^25+436x^26+384x^27+469x^28+192x^29+156x^30+16x^32+3x^36+1x^40

The gray image is a code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 0.172 seconds.