The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+35x^30+8x^31+107x^32+60x^33+132x^34+182x^35+255x^36+442x^37+619x^38+832x^39+930x^40+1032x^41+907x^42+844x^43+571x^44+468x^45+257x^46+168x^47+140x^48+44x^49+79x^50+14x^51+37x^52+2x^53+17x^54+6x^56+1x^58+1x^60+1x^66

The gray image is a code over GF(2) with n=164, k=13 and d=60.
This code was found by Heurico 1.16 in 3.01 seconds.