The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+88x^70+288x^71+397x^72+628x^73+530x^74+762x^75+582x^76+738x^77+583x^78+726x^79+521x^80+578x^81+366x^82+502x^83+257x^84+226x^85+168x^86+106x^87+55x^88+30x^89+16x^90+16x^91+8x^92+4x^93+9x^94+2x^96+4x^97+1x^100

The gray image is a code over GF(2) with n=312, k=13 and d=140.
This code was found by Heurico 1.16 in 4.04 seconds.