The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+182x^71+233x^72+266x^73+198x^74+244x^75+140x^76+116x^77+145x^78+144x^79+67x^80+94x^81+61x^82+52x^83+29x^84+36x^85+19x^86+6x^87+1x^90+12x^91+1x^96+1x^100

The gray image is a code over GF(2) with n=304, k=11 and d=142.
This code was found by Heurico 1.16 in 72.1 seconds.