The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+42x^22+73x^24+140x^26+134x^28+1240x^30+230x^32+76x^34+56x^36+30x^38+15x^40+8x^42+2x^44+1x^48

The gray image is a code over GF(2) with n=120, k=11 and d=44.
This code was found by Heurico 1.16 in 70.1 seconds.