The generator matrix

 1  0  1  1  1 X+2  1  1  2  X  1  1  1  X  1 X+2  1  1  1  1  2  2  1  1  1  0  2  1  1  1  1  1  0 X+2  1  1  1  1  1  1  1  1  0  1  0  1  1  1  1  1  1  1  1  1  0  1  X  1  1  0  1  X  1  0  2  1  1
 0  1  1  0 X+3  1  X X+1  1  1 X+2  3 X+1  1 X+2  1  2  3  X X+1  1  1  0  X  3  1  1 X+3  3  1  2  2  1  1  2 X+3  0 X+3 X+3 X+3  0  3  1 X+3  1  1 X+3 X+2 X+3 X+2  X  3  1  2  1  0  X X+1 X+2  1  0 X+2 X+2  1  1 X+1  0
 0  0  X  0 X+2  0  0  0  2  2  0  2  X X+2  X X+2  X X+2  X  2 X+2  X X+2  X  0  2  X  0 X+2  0  2  X  X  X X+2  2  0  X X+2  0  0  2  2  0 X+2 X+2  X  0 X+2  0  X  0  X  X  0  X  2 X+2  2  0 X+2  X  2  2  X  X  X
 0  0  0  X  0  0  X  2 X+2  X  0  0  X  0 X+2 X+2  2  X  0 X+2  2 X+2  X  0 X+2  X  2  X  X  0  X  X X+2  X  2  0  2  0  2  X  2 X+2  2  0  X  0  0  X  X  2  X  X  X  0  2  0 X+2  2  X X+2 X+2  2 X+2  0 X+2 X+2  X
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  0  0  2  0  0  2  2  0  2  2  0  0  2  0  0  2  0  2  2  2  2  2  0  2  2  0  2  0  0  0  2  0  0  2  2  0
 0  0  0  0  0  2  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0  0  0  0  0  2  2  2  0  0  2  2  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0  0  2  0  0  0  0  2  0  0  2  2  2  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  0  2  0  0  2  2  0  2  2  0  0  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+45x^58+92x^59+232x^60+352x^61+403x^62+572x^63+644x^64+702x^65+778x^66+736x^67+765x^68+728x^69+582x^70+508x^71+326x^72+224x^73+207x^74+114x^75+58x^76+32x^77+30x^78+22x^79+13x^80+10x^81+2x^82+2x^83+9x^84+2x^87+1x^94

The gray image is a code over GF(2) with n=268, k=13 and d=116.
This code was found by Heurico 1.16 in 4.64 seconds.