The generator matrix

 1  0  0  1  1  1  0 X^2+2 X^2+2 X^2+2  1  1  1  1 X^2+X  1  1 X+2  1  X  1  X  1  X  1  1 X^2+2  1  1  1  X X^2+X  1  1  1 X^2+2  1  1 X^2  1 X^2+X+2 X+2  1  X  1  1 X^2 X^2+X X^2  1  1 X^2  1 X^2 X^2+X+2 X^2+2 X^2+X+2  1  1
 0  1  0  0 X^2+1 X^2+3  1  X  1  1 X^2+1 X^2+1 X^2+2 X^2 X^2 X^2+X+1 X^2+X  1 X+2  1 X+1 X^2+X X+3  1 X^2+X+2 X+2  1 X^2+3 X^2 X^2+X+3  1  1 X^2 X+1 X^2+X+2  2  0 X+2  1  1  1 X^2+X+2  2  1 X+3 X+2  1  1  1 X^2+X+2 X^2+X+3  0  0  1  1  0  1 X+3 X^2+1
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  3  3 X^2+X+2  X X^2+3  1 X^2+X  X X^2+2 X+3 X^2+1 X+3  1 X^2+3 X+3 X^2  3 X+2  0 X^2+3 X^2+1  X X^2+2 X+3 X^2+2  X  1 X^2+X X^2+X+3 X^2+X+1  0 X^2+X  1 X^2 X^2+X+1 X^2+X+2  1 X^2+3  1  X  2 X^2+2  1  1 X^2+X+3 X^2  1  0 X^2+X+1 X^2+2
 0  0  0 X^2 X^2  0 X^2 X^2+2 X^2  2  2 X^2+2 X^2  0 X^2 X^2 X^2+2  0  2 X^2 X^2+2  0 X^2  2  2 X^2  0 X^2+2 X^2+2  2  0 X^2  0  2  0 X^2+2  0  0  0 X^2+2  2  2 X^2+2 X^2+2  2  2 X^2  0 X^2+2 X^2 X^2+2  2 X^2+2 X^2+2  2 X^2 X^2+2 X^2+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+410x^54+1020x^55+1784x^56+1904x^57+2234x^58+2324x^59+2058x^60+1716x^61+1322x^62+728x^63+459x^64+216x^65+142x^66+20x^67+26x^68+4x^69+4x^70+4x^71+8x^72

The gray image is a code over GF(2) with n=472, k=14 and d=216.
This code was found by Heurico 1.16 in 6.19 seconds.