The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+172x^66+40x^67+463x^68+296x^69+872x^70+588x^71+1324x^72+916x^73+1564x^74+1208x^75+1713x^76+1204x^77+1532x^78+1008x^79+1157x^80+604x^81+700x^82+224x^83+376x^84+52x^85+186x^86+4x^87+101x^88+56x^90+14x^92+6x^94+1x^96+2x^100

The gray image is a code over GF(2) with n=304, k=14 and d=132.
This code was found by Heurico 1.16 in 18.4 seconds.