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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+94x^68+4x^69+284x^70+36x^71+350x^72+108x^73+386x^74+208x^75+541x^76+304x^77+446x^78+228x^79+344x^80+92x^81+202x^82+40x^83+202x^84+4x^85+102x^86+55x^88+44x^90+11x^92+8x^94+1x^96+1x^120

The gray image is a code over GF(2) with n=308, k=12 and d=136.
This code was found by Heurico 1.16 in 1.82 seconds.