The generator matrix

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

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+112x^75+709x^76+1442x^77+2403x^78+2942x^79+3614x^80+3618x^81+4178x^82+3366x^83+3376x^84+2506x^85+1805x^86+1110x^87+778x^88+392x^89+208x^90+94x^91+56x^92+24x^93+14x^94+4x^95+9x^96+2x^97+4x^99+1x^100

The gray image is a code over GF(2) with n=656, k=15 and d=300.
This code was found by Heurico 1.16 in 12.9 seconds.