The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+18x^44+32x^45+6x^46+4x^48+2x^54+1x^72

The gray image is a code over GF(2) with n=180, k=6 and d=88.
This code was found by Heurico 1.16 in 0.0281 seconds.