The generator matrix

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

generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+162x^70+718x^71+1297x^72+2264x^73+2927x^74+3334x^75+4322x^76+3746x^77+3926x^78+3166x^79+2542x^80+1800x^81+1136x^82+738x^83+323x^84+166x^85+96x^86+40x^87+17x^88+24x^89+17x^90+4x^91+1x^92+1x^96

The gray image is a code over GF(2) with n=616, k=15 and d=280.
This code was found by Heurico 1.16 in 12 seconds.