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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+160x^55+123x^56+376x^57+212x^58+448x^59+193x^60+244x^61+76x^62+100x^63+31x^64+68x^65+12x^67+3x^68+1x^96

The gray image is a code over GF(2) with n=472, k=11 and d=220.
This code was found by Heurico 1.16 in 0.265 seconds.