The generator matrix

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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+84x^70+698x^71+1219x^72+1764x^73+1697x^74+2312x^75+1917x^76+1786x^77+1456x^78+1382x^79+709x^80+650x^81+359x^82+152x^83+89x^84+66x^85+17x^86+16x^87+1x^88+6x^89+2x^90+1x^102

The gray image is a code over GF(2) with n=608, k=14 and d=280.
This code was found by Heurico 1.16 in 3.36 seconds.