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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+142x^54+46x^56+192x^57+362x^58+640x^59+256x^60+192x^61+130x^62+16x^64+70x^66+1x^112

The gray image is a code over GF(2) with n=472, k=11 and d=216.
This code was found by Heurico 1.16 in 17.6 seconds.