The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+84x^45+406x^46+690x^47+1099x^48+1576x^49+1953x^50+2654x^51+3085x^52+3118x^53+3304x^54+3396x^55+3029x^56+2682x^57+2140x^58+1386x^59+973x^60+582x^61+280x^62+160x^63+99x^64+46x^65+11x^66+2x^68+8x^69+2x^70+2x^71

The gray image is a code over GF(2) with n=216, k=15 and d=90.
This code was found by Heurico 1.13 in 12.4 seconds.