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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+136x^73+639x^74+1268x^75+1715x^76+1922x^77+2014x^78+2020x^79+1730x^80+1706x^81+1053x^82+816x^83+577x^84+324x^85+234x^86+98x^87+60x^88+22x^89+35x^90+4x^91+2x^92+2x^93+2x^95+3x^96+1x^98

The gray image is a code over GF(2) with n=632, k=14 and d=292.
This code was found by Heurico 1.16 in 3.55 seconds.