The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+41x^70+210x^71+233x^72+458x^73+328x^74+580x^75+267x^76+422x^77+202x^78+284x^79+165x^80+248x^81+135x^82+200x^83+79x^84+72x^85+56x^86+66x^87+20x^88+14x^89+5x^90+4x^91+2x^92+2x^93+1x^94+1x^96

The gray image is a code over GF(2) with n=308, k=12 and d=140.
This code was found by Heurico 1.16 in 1.06 seconds.