The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+82x^68+318x^70+314x^72+368x^74+249x^76+368x^78+213x^80+94x^82+31x^84+1x^86+2x^90+4x^92+1x^100+1x^102+1x^108

The gray image is a code over GF(2) with n=300, k=11 and d=136.
This code was found by Heurico 1.16 in 0.469 seconds.