The generator matrix

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

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+78x^44+56x^45+167x^46+196x^47+263x^48+388x^49+450x^50+586x^51+709x^52+792x^53+840x^54+864x^55+678x^56+624x^57+403x^58+348x^59+256x^60+176x^61+135x^62+44x^63+50x^64+12x^65+40x^66+10x^67+13x^68+10x^70+3x^74

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 4.68 seconds.