The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+12x^58+16x^59+12x^60+4x^62+3x^64+8x^65

The gray image is a code over GF(2) with n=232, k=7 and d=114.
This code was found by Heurico 1.16 in 49.5 seconds.