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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+50x^58+80x^59+140x^60+184x^61+206x^62+200x^63+311x^64+338x^65+378x^66+470x^67+331x^68+338x^69+263x^70+218x^71+158x^72+122x^73+94x^74+42x^75+62x^76+38x^77+26x^78+14x^79+16x^80+4x^81+6x^82+3x^84+2x^88+1x^102

The gray image is a code over GF(2) with n=268, k=12 and d=116.
This code was found by Heurico 1.16 in 1.4 seconds.