The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+35x^44+46x^45+83x^46+174x^47+200x^48+436x^49+364x^50+788x^51+540x^52+1096x^53+646x^54+1136x^55+593x^56+804x^57+342x^58+428x^59+124x^60+170x^61+67x^62+34x^63+29x^64+8x^65+20x^66+12x^68+12x^70+1x^72+2x^74+1x^76

The gray image is a code over GF(2) with n=216, k=13 and d=88.
This code was found by Heurico 1.16 in 3.22 seconds.