The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+139x^54+168x^55+481x^56+440x^57+570x^58+592x^59+528x^60+432x^61+419x^62+136x^63+131x^64+24x^65+22x^66+8x^68+1x^70+1x^72+2x^80+1x^94

The gray image is a code over GF(2) with n=472, k=12 and d=216.
This code was found by Heurico 1.16 in 0.297 seconds.