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

generates a code of length 74 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+147x^68+704x^69+1149x^70+1682x^71+1880x^72+2036x^73+1938x^74+1946x^75+1566x^76+1270x^77+838x^78+526x^79+305x^80+188x^81+80x^82+84x^83+19x^84+10x^85+9x^86+2x^88+2x^90+2x^91

The gray image is a code over GF(2) with n=592, k=14 and d=272.
This code was found by Heurico 1.16 in 3.28 seconds.