The generator matrix

 1  0  0  0  1  1  1  2  1  1  1 X+2  0  1  2  1  X  1  1  1  1  1  0  X  1  0  1  2  1  1 X+2  X  X  X  1  1  X  0  1  2  1  1  X  X  1  0  1  1  X  1  1 X+2  1 X+2  1  1 X+2  2 X+2  1 X+2  1  1  1  1  1 X+2  1  X  0  1  1  2  1  1  1  1
 0  1  0  0  X  X X+2  0  1  3  3  1  1  3  1  0 X+2  3 X+2  X  0  2 X+2  1  1  1 X+1  1 X+3 X+3  1  1  1  2  1  0  1  X  0  1 X+2  1 X+2  1  X  2  1 X+1  1  2  X  0  3  2 X+3  1  1  1  2  0  1 X+2 X+1 X+1  0  2  1  3 X+2  1  2  2  0 X+2 X+3 X+1  1
 0  0  1  0  X X+3 X+3  1 X+1 X+2  0  1  3 X+1  X X+2  1  1  3 X+1  2  0  0  3  X X+2 X+2  3  2  1 X+2 X+3  X  1  1  3  2  1 X+2 X+3  1  X  1 X+2 X+3 X+2  2  3 X+1 X+1 X+1  1 X+1  1 X+1  X X+1  X  1  1  2  2  2  2  2  1  2  0  X  X  2  3  1 X+2 X+1  2 X+3
 0  0  0  1 X+1 X+3  X  3  X X+2 X+1  3  X X+3  1  X X+2  1  X  3 X+2 X+3  1 X+1  1 X+1  2 X+1  2  0 X+2  2 X+3  3  X X+2  X  X X+1  3 X+3 X+1  2  0 X+1  1  0  X X+2  0  2 X+3  3 X+3 X+1  3  3 X+2  0  1 X+3  2  3  3  2 X+1 X+3 X+1  1 X+1 X+2  2 X+1  2 X+2  0 X+2
 0  0  0  0  2  2  2  0  2  2  2  0  0  2  0  2  0  2  2  2  2  2  0  0  2  0  2  0  2  2  0  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  0  0  2  0  0  2  0  0  0  0  0  2  2  0  0  0  0  2  2  2  2  0  2  2  0  2  0  0  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+388x^70+236x^71+804x^72+356x^73+1046x^74+390x^75+1102x^76+280x^77+842x^78+298x^79+739x^80+156x^81+614x^82+192x^83+366x^84+96x^85+170x^86+32x^87+56x^88+8x^89+12x^90+2x^91+4x^92+2x^95

The gray image is a code over GF(2) with n=308, k=13 and d=140.
This code was found by Heurico 1.16 in 3.64 seconds.