The generator matrix

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

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+424x^75+1846x^76+3056x^77+4451x^78+5540x^79+6732x^80+6766x^81+8207x^82+7294x^83+6906x^84+5104x^85+3959x^86+2326x^87+1505x^88+782x^89+358x^90+140x^91+62x^92+36x^93+16x^94+18x^95+4x^96+1x^98+2x^99

The gray image is a code over GF(2) with n=656, k=16 and d=300.
This code was found by Heurico 1.16 in 50.9 seconds.