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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+376x^74+1798x^75+3055x^76+4412x^77+5278x^78+7128x^79+7149x^80+7874x^81+7312x^82+7056x^83+4717x^84+4096x^85+2562x^86+1356x^87+768x^88+314x^89+124x^90+94x^91+14x^92+36x^93+4x^94+8x^95+4x^97

The gray image is a code over GF(2) with n=648, k=16 and d=296.
This code was found by Heurico 1.16 in 45.5 seconds.