The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  0  1  1  2  X  1  1 X+2  1  0  1  1  1  1  1  1  2  1  1  1  1 X+2  0  1  1  1  0  1  1 X+2  X X+2  0  1 X+2  1  1  2  0  1
 0  1  1  0 X+1  1  X X+3  1 X+2  1  3  0 X+1  1  2 X+3  1  1 X+2  1  1  X  1  3  1 X+3 X+3  1  2  1  0  X  2 X+2  1  1  X X+1 X+1  1  3  X  1 X+2  1  0  2  1  0 X+1  1  0 X+1
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  2  0  0  X X+2 X+2  X  2  X  2 X+2  0  0  X X+2  X X+2 X+2 X+2  2 X+2  X  0  2  0 X+2  2  0  2  0  X  2 X+2 X+2  X  2  X  2  2 X+2  X  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  0  2  0  0  0  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0  0  2  2  0  2  2  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  0  0  0  0  0  0  2  2  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  0  0  2  0  2  2  0  0  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  0  2  2  0  2  2  2  2  2  0  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  0  0  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  2  2  0  2  2  2  0  2  2  0  2  0  2  2  0  0  2  0  0  0  0  0  0  2  0  0  2  0  0  2  0  2  0  2  2  0  2  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+100x^44+32x^45+276x^46+140x^47+735x^48+472x^49+1164x^50+1020x^51+1871x^52+1400x^53+1976x^54+1408x^55+1908x^56+1032x^57+1208x^58+480x^59+602x^60+136x^61+212x^62+20x^63+118x^64+28x^66+4x^67+35x^68+6x^72

The gray image is a code over GF(2) with n=216, k=14 and d=88.
This code was found by Heurico 1.16 in 11.8 seconds.